CURRICULUM VITAE
Ibrahim Rahimov, Ph.D., Doctor of Sciences
PERSONAL INFORMATION:
Mailing Address: Department of Mathematical
Sciences
King Fahd University of Petroleum and Minerals
Phone: 966(3) 860 3174 (W) / 860 5230 (H)
Fax: 966 (3) 860 2340 (W)
E-mail:
rahimov@kfupm.edu.sa
Sex: Male
Marital Status: Married, Three
Children
Citizenship: Uzbek
MAJOR
FIELD OF SPECIALIZATION: Probability and Statistics
AREAS
OF RESEARCH INTEREST: Branching Stochastic Processes
Statistics of Branching Processes
Markov
Branching Diffusions
Random Sums
Sampling theory
A.
ESSENTIAL
BACKGROUND
A1.
EDUCATION
1991
Doctor of Physical and Mathematical Sciences
Steklov Mathematical Institute of
1976-1979 Ph.D. in
Mathematics (1979)
Romanovski Mathematical Institute of
1974-1976 M.
Sc. in Mathematics (1976),
Romanovski Mathematical Institute of
1967-1972 B. Sc. in
Mathematics
A2. EMPLOYMENT
A)
Research Positions:
1990-
Leading researcher
The Mathematical
Institute of
Uzbek Academy of Sciences (on leave)
1980-1990 Senior researcher
The Mathematical
Institute of
1974-1976 Fellow researcher
The Mathematical
Institute of
B) Positions at Universities:
01.01.2001- to date Professor of Mathematics and Statistics
Department
of Mathematical Sciences
KFUPM,
1998-2001 Associate Professor
Department
of Mathematical Sciences
KFUPM,
1996-1997 Associate Professor
School of Mathematical
Sciences
University Science
1993-1995 Full Professor
The
1991-1993
Full Professor
1990-1991
Associate Professor
The
1987-1988
Associate Professor
1977-1978
Lecturer
Tashkent Road Institute
1972-1974
Lecturer
It should be noted that the position of senior researcher in the
A3. MAJOR AWARDS AND SCHOLARSHIPS
1. A Silver medal for achievements and excellent
results in study, Fergana , USSR
2. Romanovski Award for
the best scientific results by yang researchers, USSR
3. A grant from ISI Tokyo Session Memorial Program
to participate at 51st ISI Session. The Institute of
Statistical Research, Tokyo ,
Japan
4. Distinguished Researcher Award for 2005-2006 years, KFUPM, May, 2006.
5. Best Research Project Award for 2007-2008 years, KFUPM, May 2008.
I never had a scholarship since the education
in my country used to be free.
A4. IMPORTANT COURSE
WORKS
Successfully
completed about twenty courses
including Applied Stochastic Processes
(for PhD students), Statistical Theory I and II , Linear Models, Stochastic
Processes (for master students), Advanced Probability Theory, Mathematical
Statistics, Multivariate Statistical Analysis, Applied Statistics Finite
Mathematics, Calculus I, II and Consulting.
A5. ABOUT PH.D
AND DOCTOR OF SCIENSES THESES
a)
Ph.D. Thesis.
The
Ph. D. dissertation “Branching Stochastic Processes with Time-Dependent
Immigration” was based on the research done until 1979 and on the publications
C4, 1977 and C3, 1978 [1]-[6]. In this research first limit theorems for
branching processes with non-stationary immigration were obtained. The thesis
was defended at Romanovski Mathematical Institute in
April 1979 earlier than appointed time in the Ph.D. program. The Supervisor:
Professor I. Badalbaev.
b) Doctor of Physical
and Mathematical Sciences Thesis.
A Doctor of Sciences thesis is required to
contain at least one of the following.
It
must open a new direction in the area of the research, it must give a solution
of a difficult long standing problem or it must suggest an essentially new
method of investigation.
My Doctor of Sciences Thesis “ Summation of a
Random Number of Random Variables and Branching Stochastic Processes” is based
on the research done from 1980 to 1990. It contains a new approach to study of
branching stochastic processes based on the theory of summation of dependent
random variables. The thesis was defended in June 1991 at Steklov
Mathematical Institute of USSR Academy of Sciences. Professors B. A. Sevastyanov, V.M. Shurenkov and
V. Topchiy are Official Opponents. The Mech. Math .
Department of Moscow State University is the Refereeing Institution.
By
the Official opponents and by the Permanent Jury of Steklov
Mathematical Institute the approach suggested in the thesis was judged as a new
method of study in the theory of stochastic processes.
The Jury of Steklov
Mathematical Institute which considered my thesis:
1.
Professor Prokhorov
Yu. V., 8. Professor Gonchar A. A.
2.
Professor Nikolski S. M.
9. Professor Kozlov
V. A.
3.
Professor Stechkin S. B.
10. Professor Kudryavtsev L. D.
4.
Professor Chibisov D.
M. 11. Professor Rozanov Yu.
A.
5.
Professor Kholevo A.
S. 12. Professor Sazonov V.
V.
6.
Professor Borovkov A.
A. 13. Professor Sevastyanov B.
A.
7.
Professor Vitushkin A. G.
14. Professor Shiryayev A. N.
A6. KNOWLEDGE OF
COMPUTING
SPSS, SAS, Minitab, Statistica,
Excel, Plain
A7. WORKSHOPS/ COURSES ATTENDED
Courses of English, Turkish, Bahasa
Malay, 1993-1997
Workshop on Graphic Calculators, USM, November, 1997
Workshop on evaluating KFUPM, November, 1998
Workshop on Algebra and Applications, KFUPM October,
1999
Workshop on Geostatistics, Research Institute
KFUPM 1999
Workshop
“How to be an Effective University Teacher”. KFUPM, 2002.
A8. MEMBERSHIP IN PROFESSIONAL SOCIETIES
Elected
Member of International Stat. Institute
(
Member of American Mathematical Society (1993-present)
Extraordinary Member of Bernoulli Society (1995-present)
Member of the Union of Uzbek Mathematicians (1990- present)
Organizer of the meeting of
invited papers “Population Dynamics with Migration
Effects” at 51 st Session of the International Statistical Institute,
A9. EDITORSHIP IN MATHEMATICAL JOURNALS
Associate editor of the "Journal of
Applied Statistical Science"
( USA, 1994- ).
Associate editor of the “Journal of Statistical
Theory and Applications” (
Associate editor of “Pakistan Journal of Statistics”
(1996-)
Associate editor of the journal “Istatistik”
(Turkey, 1996-)
Referee of “Journal of Applied
Probability” (England, 1996-)
Referee of “ Advances in Applied
Probability” (England, 1996-)
Reviewer of “Mathematical
Reviews” of American Math.
Society (April 1981 - present)
B.
TEACHING
B1. TEACHING EXPERIENCES
0. .
Department of Mathematical Sciences
KFUPM,
2001-Date
1. Department of
Mathematical Sciences
KFUPM,
2.
School of Mathematical Sciences
University Science
3. The
4.
5.
The
6.
7.
Tashkent Road Institute
8.
B2. LIST OF COURSES TAUGH BY DR.
I. RAHIMOV
I.
Undergraduate Courses
1. Introductory Algebra and Number theory Fergana State University
2. Calculus I, II Fergana State University
3. Ordinary dif. Equations Fergana State University
4. Introduction to Probability and Math. Statistics. Tashkent Road Institute
5. Linear Programming Tashkent Economical University
6. Statistics I Tashkent Economical University
7. Statistics II Tashkent Economical University
8. Applied Probability Tashkent Economical University
9. Business Statistics Tashkent Economical University
10. Probability, METU, Ankara, Turkey
11. Mathematical Statistics METU, Ankara, Turkey
12. Stochastic Processes METU, Ankara, Turkey
13. Multivariate Statistics METU, Ankara, Turkey
14. Finite Mathematics KFUPM, Dhahran
15. Calculus I KFUPM, Dhahran
16. Calculus II KFUPM, Dhahran
17. Calculus III KFUPM, Dhahran
18. Probability and Statis. for Eng. and Scientists, KFUPM, Dhahran
19. Introduction to statistics KFUPM, Dhahran
20. Business Statistics I KFUPM, Dhahran
21. Business Statistics II KFUPM, Dhahran
II. Graduate Courses
1. Advanced Probability Theory
2. Stochastic Processes
3.
Statistical Theory I
METU,
4.
Statistical Theory II
METU,
5.
Applied Stochastic
Processes
METU,
6. Linear
Models
USM,
7.
Stochastic Processes
USM,
8. Applied Regression and Experimental Design KFUPM, Dhahran
B3.
Involvement in Thesis Supervision
I was involved in supervision of the following
students.
Name of
Student Degree Date
Completed
S. Kurbanov
PhD 1992
A. Teshabaev
PhD
1996
Hummieda
(USM,
Yeoh Hong Beng (USM,
H. Hasan (USM,
Kurbanov C. A. (UWB, Czech ) PhD 2006
In addition I was involved in supervision of
the following Ph.D. students
Yu. Djuraev (1983),
B4. COURSE DEVELOPMENT RESPONSIBILITIES
[1] Involved in the development of the proposed BS program with Stochastic
processes and Time Series Analysis at the Department of Mathematical
Sciences, KFUPM,
[2] Involved in the development of the proposed
MS program at the Department of Mathematical Sciences, KFUPM,
[3] Involved in the development of the proposed
Ph.D. program at the Department of Mathematical Sciences, KFUPM. Responsible in
developing a core course of “Advanced
Probability Theory” and few elective courses.
B5 COMPUTING ABILITIES
I try to use educational aids in my teaching
process. I have been using the following computer software in teaching of
various courses: SPSS, SAS, Minitab, Statistica,
Excel, Plain Tex, Latex, Microsoft Word. In particular in my Calculus courses
at KFUPM I shove students how to create simple programs for calculators and
demonstrate possibilities of programmable calculators in solving some problems.
C. RESEARCH
C1.
Research Interests
My
research interests concern the theory, statistics and applications of branching
stochastic processes and diffusions, sampling sums of dependent variables,
random sums, and sums of dependent indicators.
The following could be considered as my basic scientific results:
(a) Proposing a new
scheme of proof of limit theorems for sums of a random number of random
variables. Demonstration possibilities of this scheme in the case of infinitely
divisible limit distributions and sampling sums of dependent variables.
(b) Developing a
unified approach to immigration problems in branching processes based on a
general limit theory for random superposition of copies of stochastic
processes.
(c) Investigation of
new functionals of branching processes concerning their genealogical trees,
records, exceedances and extreme of family sizes.
These
results are included in my Doctor of Physical and Mathematical Sciences
thesis submitted in Steklov Mathematical Institute and have been published in
the following monographs and articles.
C2. Summary of Research
I have been actively engaged in research since 1977. My research
contribution can be categorized into the following:
1.
Sampling
Theory and Random Sums.
2.
Sums
of Dependent Indicators.
3.
Immigration
Problems in Branching Processes.
4.
Functional
Limits and Extreme of Branching Processes
5.
Estimation
Theory for Branching Processes
1.
Sampling
Theory and Random Sums
It is known that many characteristics of branching stochastic processes can be
represented as sums of random number of random variables or random fields. I
have suggested a new approach to study such sums based on an idea of their
representation as sampling sums of dependent random variables. It turned out
that, if we apply this representation to simple random sums, we obtain almost
all known and many new results for random sums directly from the
representation. Moreover, this representation allows to study branching
processes with immigration in cases when reproduction and immigration processes
are not independent. It was impossible to treat the latest case by traditional
methods of the theory based on generating functions ( see monograph [18], Ch.
I, and articles [13], [16] and [17]).
It is known that the sum of n random variables randomly selected from a finite population 
,
,
of independent random variables in the equiprobable 
scheme
of sampling without replacement can be represented as
,
where 
random
variables taking values 0 or 1. Here 
and
are
independent. Let now vectors 
and
are
not independent. It is clear that this scheme (under some assumptions)
includes, for example, the case when the decision about including variable into
the sum depends on the values of 
.
For such generalized sampling sums I have obtained necessary and sufficient
conditions to have a limit distribution, have given an approximation for their
distributions and have obtained uniform and non-uniform estimates of the rate
of convergence ( see monograph [18 ],Ch. I, papers [2], [5], [9] and
[16]).
Necessary and sufficient conditions are obtained for sums of
randomly indexed stochastic processes to have a limit distribution in the case
when the sequence of indexes and the initial sequence of stochastic processes
are not independent. These conditions are extensions of well-known Anskombe
condition to the above sums (see monograph [18] , Ch. I, paper [11] ).
Several new estimators are proposed for the population mean, based on the
ranked sets of samples with random set size and random number of replications.
It is demonstrated that in most cases these estimators are better than existing
ones. Conditions for asymptotic normality of those estimators are obtained.
(Papers [34], [35]).
2.
Sums
of Dependent Indicators
Sums of dependent indicators appear in many problems of the probability theory,
such as random allocations, queueing theory, branching processes and so on. The
study of such sums needs a new techniques in each case of dependence. I have
considered two kinds of dependent indicators: the case of multivariate
functions of independent random variables and the case of arbitrary dependence.
Considering sum of a random number of indicators I have found conditions for a
Poisson approximation of the distribution and have given an estimation of the
rate of convergence in this approximation. This is in the case of first kind of
dependence. In the case of arbitrary dependence I have found approximation of
the distribution by a mixture of normal distributions. (Monograph [18], Ch. IV,
papers [4], [10].
We must note that models considered in the above two directions are not simple
generalizations or extensions of known schemes. They are constructed and
investigated in connection with various concrete problems in stochastic
processes. Hence they found their non-trivial and interesting applications in
the directions which we are going to present below.
1. Immigration Problems
Over the last decade I have developed a unified approach to immigration
problems in branching stochastic processes. This approach is based on
developing a general limit theory for random superpositions of copies of
stochastic processes. Since branching processes maintained by immigration
comprise particular cases of this general set-up, it provides a unified
approach to a variety of problems that had previously been treated in
isolation. Moreover, this approach allows to study new models of the
immigration process depending of reproduction, that was impossible to treat by
traditional methods based on analysis of probability generating functions.
Construction, development and applications of this approach can be seen in my
monograph [18], Ch. I and II, and in articles [12], [13], [15] and [22]..
In the
case of non-stationary immigration process a perfect description of the
asymptotic behavior of the number of particles have been constructed. Some new
properties of the limit behavior of the process have been discovered and the
causes of these effects are explained. Local limit theorems in the
“non-classical” situation (when non-degenerate limit distributions for the
number of particles come out by functional non-linear normalization) are also
proved. These results which are published in monograph [18], Ch III and in
papers [3], [7], [8] and [14 ] have been applied in investigation of
various problems in Biology [25 ], [27], in Physics [26], and other areas.
4.
Functional
Limit Theorems and Extreme of Branching Processes
The main object of investigation in the theory of branching processes is the
number of individuals (particles) at a given time. Since this number can be
represented as sum of independent processes “shifted” over time, the problem
can be reduced to the analysis of equations for probability generating
functions. However there are many other characteristics of the process which
can not be written as such sums and, therefore, can not be treated by the
generating function techniques. Applying result obtained for sums of dependent
indicators (see part 2), makes possible to study various new characteristics of
branching processes concerning their genealogy. Connections of these
characteristics with problems of allocation of particles into cells are also
established. (see [18], ch IV and papers [4] and [10]).
Extreme problems concerning branching processes, such as maximum of family
sizes in the process, records, exceedances and the number of productive
individuals in the branching processes are stated and methods for study of
these processes are developed. (Papers [19], [20], [21], [23], [24] and [29]-[31]).
One natural approach to study of extremes in branching processes is using limit
theorems in the functional form. Using a martingale approach the functional
limit theorems are established for critical and nearly critical processes with
time-dependent immigration. (Papers [32], [33])
5.
Estimation
Theory for Branching Processes
Estimation theory of parameters of branching processes is very important part
of statistical theory for stochastic processes. Since properties of branching processes
strictly depend on the average number of descendants of one individual, it is
important to give an estimator for it based on observed values of the process.
However, in the critical and sub critical cases it is difficult, because such
processes extinct with probability 1. One of ways to avoid this difficulty is
to consider processes with immigration. But, if we consider a stationary
immigration, in the critical and sub critical cases the process may be
suppressed by immigration. Therefore it is better to consider decreasing or
state-dependent (more complicated) immigration component. Considering sub
critical processes with state-dependent immigration I have given
consistent and asymptotically unbiased estimators for the offspring and immigration
averages. It was also shown that these estimators are asymptotically normal. I
have proposed new consistent and asymptotically unbiased estimators for the
expectation and variance of the limit distribution and also for the
probability of hitting the state zero by the process. These results were
published in [6]. One may observe a rise of interest to this kind problems
after more than ten years [28]. It was known that the conditional
least squares estimator (CLSE) of the offspring mean in a branching process
with stationary immigration is not asymptotically normal. Later it was proved
that if the offspring variance tends to zero, it has normal limiting
distributions. Note that the condition that the offspring variance tends to
there means that in the long ran the process approaches to deterministic
process. In recent investigations we proved asymptotic normality of the CLSE
when the offspring variance does not tend to zero in non classical model. We
were able to show this using functional limit theorems , which are
discussed above. (Papers [32], [33])
REFERENCES
[1]* Rahimov, I., On the limit
theorems for a sequence of branching processes with non-homogeneous
immigration. THEORY OF PROBAB. AND APPL. 1984, N4, (Russian and English
trans.).
[2] Rahimov, I., Uniform
estimates in the limit theorems for branching processes with immigration,
IZVESTIYA of AS of UzSSR 1984, No4, 24-29 (Russian).
[3]* Rahimov, I., Critical
branching processes with infinite variance and decreasing immigration. THEORY
OF PROBAB. AND APPL. 1986, v.31, No1, 98-110 (Russian and English ).
[4]* Rahimov I., Limit
theorems for random sums of dependent indicators and their applications in the
theory of branching processes. THEORY OF PROBAB. AND APPL. 1987,
v.32, N2, 317-326, (Russian and English)
[5] Rahimov, I., On
approximation of the distribution of the sum of a random number of random
terms, DOKL.of AS of UzSSR, 1987, No1, 5-7 (Russian).
[6] Rahimov, I., Statistical
estimates for parameters of a subcritical Galton-Watson processes with a
reflecting screen. “PROBABILITY MODELS AND MATHEM. STATIST.” Tashkent,
1987, 76-87 (Russian.).
[7]* Rahimov, I., Local limit
theorems for branching random processes with decreasing immigration. THEORY
OF PROBAB. AND APPL. 1988, V.33, No2, 387-392 (Russian and English trans.).
[8] Rahimov, I., A local
theorem for Galton-Watson processes with immigration in the case of uniform
limit distribution, ”SERDICA” , 1988. V14, No3, 234-244 (Russian).
[9]* Rahimov, I.,
Sirazhdinov S. Kh., Approximation of distribution of a sum in a certain
scheme for summation of independent random variables. SOVIET MATH. DOKL.
Vol.38, 1989, No1, 23-27 (English)
[10]* Rahimov, I.,
Asymptotic behavior of families of particles in branching random processes. SOVIET
MATH.DOKL.,Vol.39, 1989, N2, 322-325 (English).
[11] Rahimov, I.,
Asymptotic behavior of the sum of randomly indexed processes, In the book
“ASYMPTOTIC PROBLEMS OF PROBABILITY THEORY AND MATH. STATIST.” “Fan”, Tashkent,
1990, 79-92 (Russian).
[12]* Rahimov, I., The General
branching processes with immigration depending on reproduction, THEORY OF
PROBAB. AND APPL., 1992, V. 37, No 3, 513-525 (Russian and English ).
[13]* Rahimov, I., Sampling
sums of dependent random variables, mixtures of infinitely divisible laws and
branching random processes, DISCRETE MATH. AND APPL.,
1992, V.2, No3, 337-356 (English).
[14]*Rahimov, I.,
Critical Processes with infinite variance and increasing immigration ,
MATHEMATICAL NOTES, 1993, V.53, No 6, P.97-107, (Russian and English ).
[15]* Rahimov, I., Branching
Processes as a Sums of Dependent Random Variables., BRANCHING PROCESSES,
First World Congress, 1993, Varna, Bulgaria. Springer-Verlag,
Ser. LNS, Vol. 99, 1995, p. 58-66, Editor Ch. Heyde, (English).
[16]* Rahimov, I., Weak
convergence of certain multiple sums of dependent random variables.
Probabilistic Methods in Discrete Mathematics, Progr. Pure Appl. Discrete
Math., 1, VSP, Utrecht, 1993, 376-385 (Russian and English).
[17] Rahimov, I., Mixtures of
Infinitely Divisible Laws as Limit Distributions for a Special Form Multiple
Sums, UZBEK MATHEMATICAL JOURNAL, 1994, No 4, P. 43-50 (Russian).
[18] Rahimov, I., Random Sums and Branching Stochastic
Processes, SPRINGER VERLAG, LNS, V. 96, 1995. (English).
[19]* Rahimov, I., Record
values of a family of branching processes, Classical and Modern Branching
Processes, Springer-Verlag, Ser.”IMA Volumes in Mathematics and its
Applications”, Vol. 84, 1996, Editors K. Athreya and P Jagers, P. 285-295.
(English).
[20]* Rahimov, I., Yanev, G., Maximal Number of Direct Offspring
in Simple Branching Processes, NONLINEAR ANALYSIS, 1997, V.30, No
4, p.2015-2023. (English),
[21]* Rahimov, I., Kassim, S. Record Values Concerning a
Family of Age-Dependent Processes, THE BULLETIN OF THE MALAYSIAN
MATHEMATICAL SOCIETY, 1997, Vol. 20, No. 2, 57-66. ( English).
[22]* Rahimov, I., Multitype
Processes with Reproduction-Dependent Immigration, JOURNAL OF APPLIED
PROBABILITY, 1998, V. 35, No. 2, P. 281-292 (English).
[23]* Rahimov, I.,
Yanev, G., On Maximum Family Size in Branching Processes, JOURNAL OF APPLIED
PROBABILITY, (Accepted for publication, will appear in 1999, English).
[24]* Rahimov, I., Hasan,
H., Limit Theorems for Exceedances of a Sequence of Branching Processes,
THE BULLETIN OF THE MALAYSIAN MATHEMATICAL SOCIETY, (Accepted for
publication, will appear in 1999, English).
[25] Berlin, Y. A., Drobnitsky, D., O., et
all., On Inherited Fertility in Biological Systems, Biosystems, 1992, V. 26,
No. 3, p. 185-192.
[26] Berlin, Y. A., Drobnitsky, D., O., et
all., Correlated Fluctuations in Multielement Systems, Physical Review A, 1992,
Vol. 45, No. 6, p. 3547-3552.
[27] Lange, K., Fan, R., Z., Branching Process
Models for Mutant-Genes in Nonstationary Populations. Theoretical Population
Biology, 1997, V. 51, No. 2, P. 118-133.
[28] Jacob C., Peccoud J.,
Estimation of the Parameters of Branching Process from Migration Binomial
Observations, Advances in Applied Probability, 1998, V. 30, No. 4, p.
948-967.
[29]* Rahimov I.
Approximation of exceedance processes in large populations. Stochastic Models,
2001, (ISI), V. 17, No 2, P. 147-156.
[30] * Rahimov I. Random Sums
of Independent Indicators and Generalized Reduced Processes. Stochastic
analysis and applications, (ISI) Vol. 21, No 1, 2003, P. 205-221.
[31]* Rahimov I., Limit Theorems for the size of Subpopulation of
Productive Individuals. Stochastic models, (ISI) VOL. 20, 2004, no 3, P.
261-280.
[32]* Rahimov I., Functional Limit Theorems for Critical Processes with
Immigration "
Advances in Applied Probability, 2007, V. 39, No 4,
P.
1054-1069
(ISI)
[33]* Rahimov I. Asymptotic distribution of the CLSE in a critical
process with
Immigration. Stochastic Processes and Their Applications, 2008,
Vol. 118, 1892-1908. (ISI).
[34]* Rahimov I.,
Muttlak H. A. Estimation of the population mean using random selection in
ranked set samples. STATISTICS AND PROBABILITY LETTERS, (ISI) Vol 62, 2003, P.
203-209.
[35]* Rahimov I., Muttlak H. A. Investigating the Estimation of
the Population Mean Using Random Ranked Set Samples. NONPARAMETRIC STATISTICS,
2003, V 15, No 3, P. 311-324.
C3. Works in Progress
My current research concerns the following
directions.
a)
Multivariate Random
Sums.
Let 
be a random sum of 
random vectors ,
where are not necessarily independent of .
In the case when are random variables and are stopping times with respect to the
filtration generated by ,
it was shown that the investigation of the random sum 
could be reduced to study of a simple sum of
dependent variables (see Monograph [1]
C3). It is interesting to consider such a problem in the case of random
vectors. Results, which are going to be obtained in this direction, will be
applied in investigation of sampling sums of dependent vectors, multivariate random
walks, random fields and multitype general branching
processes.
b) Immigration-Branching Diffusions
Immigration-Branching
Diffusions are models of a population process in which offspring move at random
on a bounded space throughout their lives according to diffusions. Each member
of the population at the end of its life generates a new population whose
members may be located at any point of the space. In addition a random number
of new particles may immigrate into the population. Currently the theory of
such processes contains many results in the case when diffusion, reproduction
and immigration processes are independent. It is important to develop methods
of investigation for processes allowing dependence of the above three
components. Here I hope that an approach suggested in the article [1], 1992, C4 and in the book [1], C3 will allow to consider such a
generalization.
b)
Extreme Concerning
Branching Processes
First
results on the size of largest family in Galton-Watson processes were obtained
in the paper [2], 1997, C4 (see also
[3], 1998, C4). Similar problem for Galton-Watson processes allowing
immigration have been considered jointly with my student H. Hummieda.
In this direction there are many interesting problems, such as to consider more
general models of processes or to consider k-th
maximal family and other problems.
Another
class of problems is to study exceedances and record
properties of a sequence of branching processes. First results are obtained in
publications [1] 1996, [4] 1997, [2]
1998 C4 and [1], 1996 C6. In particular, investigation of exceedances
in this model is a part of Ph.D. program of my student H. Hasan.
C4. Books
[1] Rahimov,
[2] Badalbaev,
I., S., Rahimov, I., Non-Homogeneous Flows of
Branching Processes, Tashkent, “FAN”, 1993, (Russian)
C5.
Articles Published or Accepted in
Refereed Journals
Until 1991, because of well-known situation in the
former
1978
[1]*
[2] Badalbev
I,.
[3] Badalbaev,
I., Rahimov,
[4] Rahimov,
[5] Rahimov,
[6] Rahimov,
1979
[1] Ibragimov, R., Rahimov,
[2]
[3] Rahimov,
I., Supercritical processes with immigration decreasing intensity, In the book
“LIMIT THEOREMS, RANDOM PROCESSES AND APPL., “Fan”,
1981
[1] Badalbaev
I., Rahimov, I., Two limit theorems for
Bellman-Harris processes with immigration, In the book “LIMIT THEOREMS FOR RANDOM
PROCESSES AND STATISTICAL INFERENCES”, “Fan”, Tashkent, 1981, 19-29 (Russian).
[2] Rahimov,
[3] Rahimov,
[4] Rahimov, I., Transient phenomena in branching
random processes with immigration, IZVESTIYA of AS of UzSSR,1981,No5, 30-35 (Russian).
[5] Rahimov,
1982
[1] Rahimov,
1983
[1] Rahimov, I.,Subcritical
processes with non-homogeneous immigration, IZVESTIYA of AS of Uz SSR, 1983,No3, 14-19, (Russian).
[2]*
1984
[1]* Rahimov,
[2] Rahimov,
I., Limit theorems for total number of particles in critical Galton-Watson
processes with immigration, In the book “ASYMPTOTIC
PROBLEMS OF PROBABILITY DISTRIBUTIONS”,
“Fan”, Tashkent, 1984, 106-119
(Russian).
[3] Rahimov,
I., Uniform estimates in the limit theorems for branching processes with immigration,
IZVESTIYA of AS of UzSSR
1984, No4, 24-29 (Russian).
[4] Rahimov,
[5] Rahimov,
1985
[1] Badalbaev,I. ,Rahimov,
I., New limit theorems for multitype branching
processes with immigration decreasing intensity, IZVESTIYA of AS of UzSSR, 1985, No2, 17-22, (Russian).
[2] Rahimov,
[3] Rahimov,
1986
[1]* Rahimov,
[2] Rahimov,
[3] Rahimov, I., Asymptotic behavior of the probability of hitting a fixed state
for Galton-Watson processes with
decreasing immigration, I, IZVESTIYA of
AS of UzSSR, 1986, No2; 33-38 (Russian).
[4] Rahimov,
I., Asymptotic behavior of probability
of hitting a fixed state for Galton-Watson processes with decreasing
immigration, II, IZVESTIYA of AS of UzSSR, 1986, No3,
38-46 (Russian).
1987
[1]*
[2] Rahimov,
I., On approximation of the distribution of the sum of a random number of
random terms,
[3] Rahimov,
[4] Rahimov
I., Salahitdinov R., Some generalizations of limit
theorems for Galton-Watson processes with infinite variance and decreasing
immigration, IZVESTIYA of AS of UzSSR, 1987, No3, 25-30
(Russian).
[5]
[6] Rahimov,
[7] Rahimov,
[8] Rahimov,
1988
[1]* Rahimov,
[2]* Rahimov,
[3] Rahimov,
[4] Rahimov,
[5] Rahimov,
I., Sirazhdinov,
[6] Rahimov,
1989
[1]* Rahimov,
[2]* Rahimov,
[3]* Rahimov,
[4]* Rahimov,
[5] Rahimov,
[6] Rahimov,
[7] Rahimov,
1990
[1] Rahimov,
1991
[1]* Rahimov,
1992
[1]* Rahimov,
I., The General branching processes with immigration depending on reproduction,
THEORY OF PROBAB. AND APPL., 1992, V. 37, No 3, 513-525 (Russian and English ).
[2]* Rahimov,
[3] Rahimov,
I., Critical Bellman-Harris processes with infinite variance and decreasing
immigration, UZBEK MATHEMATICAL JOURNAL,
1992, No2, 22-31 (Russian).
[4] Rahimov,
1993
[1]*Rahimov,
1994
[1] Rahimov,
I., Kurbanov, S., Subcritical
Branching Processes with Decreasing Immigration and Infinite Variance, UZBEK MATHEMATICAL JOURNAL, 1994, No 1, P.
51-57 (Russian).
[2] Rahimov,
1996
[1]* Rahimov, I., Teshabaev,
A., Decomposable branching processes with decreasing immigration, JOURNAL OF APPLIED STATISTICAL SCIENCE, 1996, V.3, No 2/3, P.169-190, (
English).
[2]* Rahimov,
1997
[2]* Rahimov,
1998
[1]* Rahimov,
I., Multitype Processes with Reproduction-Dependent
Immigration, JOURNAL OF APPLIED
PROBABILITY, 1998, V. 35, No. 2, P. 281-292 (English).
[2]* Rahimov,
I., Hasan, H.,
Exceedance
Problems Concerning a family of Branching Processes, PAKISTAN JOURNAL OF STATISTICS, 1998, V.14, No. 1, P. 37-47 , (English).
[3]* Rahimov,
[4]*
1999
[1]*
Rahimov, I., Yanev, G., On
Maximum Family Size in Branching Processes, JOURNAL OF APPLIED
PROBABILITY, V.36, No 3, p. 632-643
(English).
[2]*
Rahimov,
2000
[1]* Rahimov, I., A Limit Theorem for Multitype
General Branching Processes with Generalized Immigration, JOURNAL OF APPLIED STATISTICAL SCIENCES, V.9,
No 2, 2000, P.105-122. ( English).
[2]*
Rahimov I., On the Non-Extinction Probability of
Branching Diffusions, JOURNAL OF APPLIED
STATISTICAL SCIENCES, V.9, No 3, 2000, P. 223-236. (
English).
[3]*
2001
[1]* Rahimov I. Approximation of exceedance processes in large populations. STOCHASTIC MODELS, V. 17, No 2, P. 147-156.
[2]*
[3]*
2002
[1]*
[2]*
2003
[1] *
[2]*
[3]*
[4]*
[5]* Rahimov
I.
2004
[1]* Rahimov I., Malik
M. Asymptotic Bahavior of Expected Record Values. PAK. JOURNAL OF STATISTICS,
Vol 20, 2004, No. 1, P. 129-135 .
[2]*
[3]*
[4]* Rahimov I. On the Number of Large
Families in a Branching population. Dynamical
Systems and Applications-2004, Proceedings of the International Conference, Antalya, Turkey, July 5-10,
2004, GBS Publishers & Distributors, P. 582-597.
2007
[1]* Rahimov I., Asymptotic Behaviour of a Controlled Branching Process with Continuous State Space. STOCHASTIC ANALYSIS AND APPLICATIONS, (ISI) 2007, V. 25, No 2, P. 337-352.
[2]* Rahimov I. On a Stochastic Model for Continuous Mass Branching Population. MATHEMATICS AND COMPUTERS IN SIMULATION" (ISI ), 2007, V 76/1-3, P. 171-176.
[3]* Rahimov I., Kurbanov S. On the Number of Productive individuals in the Galton-Watson Process with Immigration. MATHEMATICS AND COMPUTERS IN SIMULATION" (ISI ), 2007, V 76/1-3, P. 177-180.
[4]* Rahimov I., Functional Limit Theorems for Critical Processes with Immigration
ADVANCES IN APPLIED PROBABILITY, 2007, V. 39, No 4, P. 1054-1069 (ISI)
[5]* Rahimov I., Sabah W. Controlled branching processes with continuous states. JOURNAL OF APPLIED PROBABILITY AND STATISTICS, 2007, V 2, no 2, 123-137.
2008
[1]* Rahimov I., Sabah W. Limiting behavior of a generalized branching process with immigration. STATISTICS AND PROBABILITY LETTERS, 2008, V. 78/3, 225-230 (ISI)
[2]* Rahimov I., Chanane B. Branching processes with incubation. STOCHASTIC MODELS, (ISI) V. 24, No 1 , 2008 , P. 71 - 88 .
[3]* Rahimov I. Asymptotic distribution of the CLSE in a critical process with
Immigration. STOCHASTIC PROCESSES AND THEIR APPLICATIONS, (ISI) V 118, 1892-1908.
[4]* Rahimov I. Two-type branching processes with sub-exponential life-spans and SIR epidemic models. STOCHASTIC ANALYSIS AND APPLICATIONS, 2008, V. 26, No 5, 925-940, (ISI) .
[5]* Rahimov I., Malik M. Records Generated by a Sequence of Branching Processes with immigration. JOURNAL OF APPLIED STATISTICAL SCIENCE, 2008, V.16, No 1, P. 27-36.
[6]* Rahimov I. Large families and exceedances in branching processes, Invited chapter for the book "RECORDS AND BRANCHING PROCESSES", 2008, Ch. 5, P. 101-122, Nova Science Publishers Inc. (USA) .
[7]* Rahimov I. Deterministic approximation of a sequence of nearly critical
branching processes. STOCHASTIC ANALYSIS AND APPLICATIONS, 2008, V. 26, No 5, 1013-1024, (ISI) .
2009
[1]* Rahimov I. Limit distributions for weighted estimators of the offspring mean in a branching process. TEST (ISI), Published online at http://dx.doi.org/10.1007/s11749-008-0124-8 .
[2]* Rahimov I. Asymptotically normal estimators for the offspring mean in the
branching process with immigration. COMMUNICATIONS IN STATISTICS:THEORY AND METHODS, 2009, V. 38, No 1, P. 13-28 (ISI).
[3] Rahimov I. Approximation of fluctuations in a sequence of nearly critical branching processes. STOCHASTIC MODELS, (ISI) (submitted).
[4] Rahimov I., Omar M. Validity of the bootstrap in the critical process with a non-stationary immigration. JOURNAL OF NONPARAMETRIC STATISTICS (ISI) (submitted).
[5] Rahimov I. Bootstrap of the offspring mean in the critical process with a non-stationary immigration. STOCHASTIC PROCESSES AND THEIR APPLICATIONS (ISI) (submitted)
[6] Abu-Dayyeh W., Rahimov I. An identity for the exponential family model. JOURNAL OF PROBABILITY AND STATISTICAL SCIENCE. (accepted).
C6. Dissertations
[1] Limit Theorems for
Branching Processes with Time-Dependent Immigration, Tashkent, 1978, (PhD Thesis,
Russian).
[2] Limit Theorems for
Branching Processes with Time-Dependent Immigration, (Abstract of PhD Dissertation), Romanovski
Math. Institute,
[3] Summation of a Random
Number of Random Terms and Branching Stochastic Processes, Steklov Math. Institute,
[4] Summation of a Random
Number of Random Terms and Branching Stochastic Processes (Abstract of Doctor of Science Dissertation), Steklov
Mathematical Institute
C7.
Papers or Abstracts Published in Conferences
1977
[1]
1978
[1] Rahimov,
I., Critical Galton-Watson processes with increasing immigration. Proceedings of
1981
[1] Rahimov, I., Critical processes with non-homogeneous immigration. IIIth International
1982
[1]* Rahimov,
1985
[1] Rahimov,
I., Local limit theorems for Galton-Watson processes with decreasing
immigration. Abstr. Comm. International Seminar on Mathem. Modelling.and Stability of Stochastic Models. Varna, Bulgaria, 1985, (Russian).
[2] Rahimov,
1986
[1]* Rahimov,
1987
[1] Rahimov,
I., Local limit theorems for Markov branching processes in a uniform limit
distribution case. International school
“ERGODIC THEORY OF MARKOV PROCESSES”, Kizil, 1987, (Russian).
1989
[1]* Rahimov,
I., The methods of summation of random variables in theory of branching
processes. V th
International
[2] Rahimov,
1991
[1]* Rahimov,
1993
[1]* Rahimov,
I., Branching Processes as a Sums of Dependent Random Variables.,
BRANCHING PROCESSES, First World Congress, 1993,
[2]* Rahimov, I., Yildirim, F., Teshabaev,
A., Non
Homogeneous Decomposable Branching Processes., BRANCHING PROCESSES, First
World Congress, Varna, Bulgaria, 1993. Springer-Verlag,
Ser. LNS, Vol. 99, 1995, p. 67-76, Editor
Ch. Heyde, (English).
[3]* Rahimov, I., Weak convergence of certain multiple sums of
dependent random variables. Probabilistic
Methods in Discrete Mathematics, Progr. Pure Appl. Discrete Math., 1, VSP,
1994
[1]* Rahimov,
I., Branching Processes with Immigration., Fourth ISOSS Conference ,
[2]* Rahimov,
[3] Rahimov,
I., Record values of a family of branching processes, Classical and Modern Branching Processes,
IMA Workshop, (by Invitation only) June
, 1994, Springer-Verlag, Ser.”IMA Volumes in Mathematics and
its Applications”, Vol. 84, 1996, Editors K. Athreya
and P Jagers, P. 285-295. (English).
1996
[1]* Rahimov, I., Random Sums in the Theory
of Branching Processes, Second International Workshop in Stochastic Modeling and Experimental Design at St. Petersburg,
1996, P.305-309. (Invited Paper, English).
[2]* Rahimov,
I., Ahsanullah, M., Record Properties of a Family of
Branching Processes, Second
International Workshop in Stochastic
Modeling and Experimental Design at St. Petersburg, 1996, P.300-304.
(English).
[3]* Rahimov,
[4]* Rahimov, I., A Transfer Theorem for Multitype Processes and its Applications, Proceedings of
the Workshop “Recent Development in
Applied Statistics”,
[5]* Rahimov,
I., Hasan, H., On the First Exceedance
of a level by Family of Branching Processes, Proceedings of Fifth Conference on Statistical Sciences,
Vol. II, 1996, Malang, Indonesia
(English).
1997
[1]* Rahimov,
I., Yanev, G.,
Maximal Number of Direct Offspring in Simple Branching Processes, Proceedings of The Second World Congress of
Nonlinear Analysis, July 10-17, 1996, Athens, Greece, NONLINEAR ANALYSIS, 1997,
V.30, No 4, p.2015-2023. (English, Invited Paper).
[2]* Rahimov,
I., Transfer Limit Theorems for Multitype General Branching Processes, 51st
Session of the International Statistical Institute, Istanbul, August 1997,
Bulletin of the International Statistical Institute, Tome LVII, Book 2,
1997, P. 583-584.
[3]* Rahimov,
I., On a Transfer Theorem for Multitype General
Branching Processes, ATCM 97 (The Second Asian Technology Conference in Mathematics), USM, Penang, Malaysia, 1997, P.8.
[1]* Rahimov,
2001
[1]*
2004
[1]*
2005
[1]*
[2]*
Rahimov I. On a Stochastic Model for Continuous Mass
Branching Population.Proceedings: MODELLING
2005, Third IMACS Conference on Mathematical Modelling. July 4-8, 2005, Pilsen, Szech RepublicSpecial issue of the journal "Mathematics and Computers
in Simulation" , 2007, V 76/1-3, P. 171-176. (ISI journal).
2007
[1]*
[2]*
Rahimov I. Convergence of the immigration-branching process and conditional
least-squares. WORKSHOP ON STOCHASTIC MODELLING
IN POPULATION DYNAMICS, April 10-14, 2007,
2008
[1]* Rahimov I. A deterministic approximation of
the branching stochastic process and applications. SYMPOSIUM ON
GLOBAL ANALYSIS AND PROBABILITY, May 26-30, 2008, Gaseem,
KSA
[2]*
[1]* Rahimov I. A branching stochastic model with incubation, THE THIRD INTERNATIONAL CONFERENCE ON MODELING, SIMULATION and APPLIED OPTIMIZATION, January 20-22, 2009, AUS, Sharjah, UAE.
[2]* Rahimov I. Weighted CLSE of the offspring mean in a non-homogeneous branching process, THE THIRD INTERNATIONAL CONFERENCE ON MODELING, SIMULATION and APPLIED OPTIMIZATION, January 20-22, 2009, AUS, Sharjah, UAE.
[3]* Rahimov I. Approximation of a sum of martingale-differences generated by a bootstrap branching process. WORKSHOP ON BRANCHING PROCESSES AND THEIR APPLICATIONS, April 20-23, 2009, Badajoz, Spain.
C8. Technical
Reports
[1] Rahimov,
I., Yanev, N., On a Maximal Sequence Associated with
Simple Branching Processes, Preprint, No. 6,
PP. 14, August 1996, Institute of Mathematics with Computer Center of
Bulgarian Academy of Sciences, Sofia, Bulgaria, (English).
[2] Rahimov,
I., Hasan, H., Exceedance
Problems Concerning a Family of Branching Processes, Tech. Report No M9/96,
November 1996, P.P.S.M., USM, Malaysia
(English).
[3]
Rahimov, I., Towards the Extinction of Immigration-Branching Diffusion
Processes, Tech. Report No M10/1997, November 1997, P.P.S.M., USM,
[4]
Rahimov,
[5] Rahimov,
[6] Rahimov, I., Muttlak, H. A. Random Ranked Set Samples, Tech. Report No 256,
May, 2000, Dep. Math. Scien. KFUPM (English).
[7] Rahimov, I., Muttlak,
H. A. Random Ranked Set Samples with Imperfect Judgment Ranking, Tech.
Report No 257, October, 2000, Dep. Math. Scien.
KFUPM (English).
[8] Rahimov I., Muttlak H. Random sums of random vectors and multitype families of productive individuals, Tech Report No 316, April, 2004 Dep. Math. Sciences, KFUPM. (English).
[9] I. RAHIMOV and W. AL-SABAH Branching Processes with Continuous Space of States No 355, May 2006, Dep. Math. And Statistics, KFUPM (English).
[10] Rahimov I, Chanane B.Branching processes with incubation , May 2007, No 376, Dep. Math. And Statistics, KFUPM (English).
[11] Rahimov I. Convergence of a non-homogeneous immigration-branching process: May 2007, No 376, Dep. Math. And Statistics, KFUPM (English).
C9.
Papers Submitted for Publication
[1] Rahimov I.
Random Sums of Independent Indicators and Generalized Reduced Processes, Stochastic
Analysis and Applications (
C10. Invited Papers and Talks
[1]* Rahimov,
[2]* Rahimov, I., Yanev,
G., On the Maximal Number of Direct Offspring in Branching Processes, Proceedings of The Second World Congress of Nonlinear
Analysis, July 10-17, 1996, Athens, Greece, (English, Invited Paper).
[3]* Rahimov,
I., A Transfer
Theorem for Multitype Processes and its Applications,
Proceedings of the Workshop “Recent
Development in Applied Statistics”,
[4]* Rahimov,
I., Random Sums in the Theory of Branching
Processes, Second International Workshop in Stochastic Modeling and Experimental Design at St. Petersburg,
1996, P.305-309. (Invited Paper, English).
[5]* Rahimov I. Immigration-Branching Diffusions and their
extinction, International
Conference on Applied Statistical Sciences V, New Jersey, USA, May 2001, Applied
Statistical Science Vol. V, 2001, P. 97-117 (Invited paper, English)
[6]* Rahimov I. On a Stochastic Model for Continuous Mass Branching Population. MODELLING 2005, Third IMACS Conference on Mathematical Modelling.
[7]* Rahimov I. Age-dependent branching processes with incubation. WORKSHOP ON STOCHASTIC MODELLING IN POPULATION DYNAMICS, April 10-14, 2007, Marseille, France.
[8]* Rahimov I. Convergence of the immigration-branching process and
conditional least-squares. WORKSHOP ON STOCHASTIC MODELLING IN POPULATION DYNAMICS, April 10-14, 2007, Marseille, France.
[9]* Rahimov I. A deterministic approximation of the branching stochastic process and applications. SYMPOSIUM ON GLOBAL ANALYSIS AND PROBABILITY, May 26-30, 2008, Gaseem, KSA
[10]* Rahimov I., Omar M. Bootstrap for critical branching process with non-stationary immigration, XIII INTERNATIONAL SUMMER CONFERENCE
ON PROBABILITY AND STATISTICS June 21-28, 2008, Sozopol, Bulgaria
[11]* Rahimov I. Approximation of a sum of martingale-differences generated by a bootstrap branching process. WORKSHOP ON BRANCHING PROCESSES AND THEIR APPLICATIONS, April 20-23, 2009, Badajoz, Spain.
C11.
Seminars
1.
From
1978 to 1993 I have given one or two
seminars a year at Romanovski Mathematical Institute
of Uzbek Academy of Sciences.
During
those years I have
also given at least one seminar a year at
2.
In 1984 and 1989-1991 I have given one seminar
a year at Steklov Mathematical Institute of Academy
of Sciences of The USSR.
In 1990 I gave a seminar at
In 1991 I gave a seminar at
3.
From 1993 to 1995 I have given one seminar a
year at Middle East Technical University, Ankara, Turkey.
In 1993 gave seminars at Khojitepa
and Gazi universities,
5.
In June of 1994 I gave a seminar on Record
Values at Minnesota University, Minneapolis, USA.
6.
In 1996 I gave a series of seminars at
University of Science Malaysia, Penang.
In 1996 I gave a seminar at Singapore National
University, Singapore.
In 1997 I gave a seminar at University Kebangsaan, Kuala Lumpur, Malaysia.
7.
In 1998 I gave a seminar on “Effect of
Migration in Stochastic Population Processes”
at KFUPM, Dhahran.
8.
In February 28, 1999 I gave a seminar on “A
Remark on Simple Random Sums” at KFUP, Dhahran.
9.
In
C12.
Research Project and Grants
1980-1993
Research
project "Limit Theorems for Stochastic Processes and Statistical
Inference", Part 1: "Limit
Theorems of the Theory of Branching Processes".
During
these years my research activity was funded by Uzbek Academy of Sciences and
Academy of Sciences of the USSR.
1988
Two weeks visit Varna, Bulgaria including speaking at a Summer School,
funded by
1994-1995
Advanced Fellowship in the NATO-CP Science Fellowship Program, 24
months,
1992
Two weeks visit
1993
Two weeks visit Varna, Bulgaria, funded by TUBITAK, Turkey.
1994
Two
weeks visit Minnesota University, Minneapolis, USA, including speaking at a
Conference funded by USA.
1995
One month visit
Two
weeks visit
1996-1997
Short
term (12 months) research project
"A forecasting method of defects in networks based on branching processes
" funded by the Malaysian Department of Science and Environmental
Technology (IRPA).
One week visit professor Louis Chen,
1997
Short term (12 months) Research project "Mathematical modelling of population dynamics and cascades of defects in
networks based on branching processes" funded by Malaysian Department of
Science and Environmental Technology (IRPA).
2003-2004
An
internal (15 months) Research project " Investigation of a Random Sum of Indicators with Applications
in Branching Stochastic Processes" funded by King Fahd University of
Petroleum and Minarals, No MS/SOCHASTIC/254,
(Principal Investigator,
Completed).
2005-2006
A
Fast Track (12 months) research project " Branching stochastic Processes
with Continuous State-Space and Immigration in Varying Environment" funded by
SABIC, No FT/2005-01,
(Principal Investigator,
Completed)
.
2006-2007
A Fast Track (12 months) research project
"Investigation of Branching Processes with Incubation" funded by SABIC No
FT/2006-03, (Principal
Investigator, Completed)
.
2006-2007
An internal (12 months) research project: “Functional Limit Theorems for Branching Stochastic Processes with Time-Dependent Immigration.”
MS/THEOREMS/MS335 (No IN060335). (Principal Investigator, Completed)
2008-2009
An internal (18 months) research project: “Investigation of the Validity of the Bootstrap in a Non-Homogeneous Branching Stochastic Process”
IN080396. (Principal Investigator). (In progress).
C13. List of selected Citations to papers by
[1] Jacob C., Peccoud J., Estimation of the Parameters of Branching Process from Migration Binomial Observations, Advances in Applied Probability, 1998, V. 30, No. 4, p. 948-967. ( Monograph [1] and paper [7] 1987 Totally 2 citations)
[2] Mitov, K. V. The maximum number of offspring of one particle in a branching process with state-dependent immigration, Proc. 27th Spring Conference of the Union of Bulgarian Mathematicians, Pleven, 1998, April 9-11, p. 92-97.
( paper [2], 1997)
[3] Lange K., Fan R.Z., Branching-Process Models for Mutant-Genes in Nonstationary Populations, Theoretical Population Biology, 1997, Vol. 51. No. 2, p 118-133.
( monograph [1])
[4] G. P. Yanev, N. P. Yanev Branching Processes with Two Types of Emigration and State-Dependent Immigration, In: C.C. Heyde, Y.V. Prohorov, R. Pyke and S. T. Rachev (Eds) Lecture Notes in Statistics, 114, Springer-Verlag, 1996, p. 216-227
( monograph [1])
[5] Kovalenko, I. M., Kuznetsov, N. Yu., Shurenkov V. M. Models of Random Processes. A Handbook for Mathematicians and Engineers, CRC Press, New York, 1996. ( paper [1], 1978)
[6] Dion, J. –P. Statistical inference for discrete time branching processes. In: Ed. Obretenov, A., Proc. 7th International Summer School on Prob. Theory and Math. Statistics (Varna, 1991). Sci. Cult. Tech. Publ., 1993, Singapore, 60-121.
( paper [1], 1987)
[7] Berlin, Y. A., Drobnitsky D. O., Goldanskii V. I., Kuzmin, V. V. Correlated Fluctuations in Multielement Systems-The Stochastic-Branching-Process Model, Physical Review A, 1992, Vol. 45, No 6, p. 3547-3552.
( paper [2], 1988)
[8] Berlin, Y. A., Drobnitsky D. O., Goldanskii V. I., Kuzmin, V. V On Inherited Fertility in Biological Systems-A Model of Correlated Fluctuations in the Stochastic Branching Processes, BIOSYSTEMS, 1992, Vol. 26. No. 3, p. 185-192
(the paper [2], 1988)
[9] Vatutin V. A., Zubkov A., M., Branching Processes II, Journal of Soviet Mathematics, 1993, V. 67, No. 6, p. 3407-3485
(papers [2], [3], [5],1984; [2], [3], 1985; [1], [2], [3], [4] 1986; [1], [4], [5], [6], [7], [8], 1987; [2], [3], [4], [6], 1988; [1], [5], [6], [7], 1989. Totally 23 citations.)
[10] Logunov P. L. Estimates for the Convergence Rate to the Poisson Distribution for Random Sums of Independent Indicators, Theory of Probability and its Applications, 1990, V. 35, No 3, p 587-590.
(paper [1], 1987)
[11] Sagitov S. M. A Multidimensional Critical Branching Process Generated by a Large Number of Particles of One Type, Theory of Probability and its Applications, 1990, V. 35, No 1, p. 118-130.
( paper [1], 1984)
[12] Vatutin V., Zubkov A. M. Branching Processes I, In: Probability Theory, Mathematical Statistics, Theoretical Cibernetics, Itogi Nauki I Tekhniki, Akad. Nauk USSR, /VINITI/, 1985, V. 23, p. 1-67
(papers [1], [2], [4], [5], [6], 1978; [1], [2], [3], 1979; [1], [2], [4], 1981; [1], 1983. Totally 12 citations)
[13] Yanev, G.P. and Yanev, N.M. (1999). Limit theorems for branching processes with random migration components. In: Proc. 9th International Summer School on Prob.Theory and Math. Statist. (Sozopol, 1997), Sci. Cult. Tech. Publ., Singapore.
( Monographs [1]and [2])
[14] Iosifescu, Marius, Finite Markov processes and their applications. Wiley Series in Probability and Mathematical Statistics. John Wiley & Sons, Ltd., Chichester; Editura Tehnic\u a, Bucharest, 1980. 295 pp. ISBN:0-471-27677-4
(paper [1], 1978)
[15] Badalbaev, I., S., Zubkov, A., M. Limit theorems for a sequence of branching processes with immigration, , Theory of Probability and its Applications, 1983, V. 28, No 2, p. 382-388.
(paper [3], 1978)
[16] Badalbaev, I., S., Pirimkulov Sh. P. A limit theorem for branching processes with immigration of decreasing intensity, IZVESIYA of Uzbek Academy of Sciences, 1981, No 4, p. 5-8. ( paper [1], 1978)
[17] Badalbaev I., S., Ganikhodjaev A. N., Some generalizations of limit theorems for branching processes with decreasing immigration, IZVESIYA of Uzbek Academy of Sciences, 1987, No 6, p. 3-8.
(papers [1], [2], 1978)
[18] Badalbaev I., S., Salakhitdinov R. M The rate of convergence in limit theorems for branching processes with decreasing immigration, IZVESIYA of Uzbek Academy of Sciences, 1983, No 5, p. 10-16
( paper [1], 1978)
[19] Badalbaev I., S., Salakhitdinov R. M Generalizations of limit theorems for branching processes with immigration of decreasing intensity, IZVESIYA of Uzbek Academy of Sciences, 1985, No 1, p. 1-12.
(paper [1], 1978)
[20] Badalbaev I., S., Salakhitdinov R. M., Estimates of the rate of convergence in limit theorems for branching processes with decreasing immigration, IZVESIYA of Uzbek Academy of Sciences, 1988, No 1, p. 3-8.
( paper [1], 1978)
[21] Ganikhodjaev A. N., Some generalized limit theorems for branching processes with immigration of decreasing intensity (a discrete case). IZVESIYA of Uzbek Academy of Sciences, 1988, No 5, p. 3-7.
(paper [2], 1978)
[22] K.V.Mitov, N.M.Yanev, Critical branching processes with decreasing state-dependent immigration, Compt. Rendues de l’Acad. Bul. Sci., Vol. 36, No 2., 1983.
( papers [1], [2] 1978)
[23] K.V.Mitov, V.À.Vatutin, N.M.Yanev, Kriticheskie processi Galtona-Watsona s
ubivajushcej immigraciej zavisjashchej ot sostojanija processa. Serdika –Bul. Math. Journal, Vol.10, 1984. 412-424.
( paper [1], 1978)
[24] K.V.Mitov, G.P.Yanev, Maximum family size in branching processes with state-
dependent immigration, Math. And Edu. In Math. , Proc. Of 28-th Spring Conference of UBM, 1999, 142-149.
(paper [2], 1997)
[25] K.V.Mitov, V.A.Vatutin, N.M.Yanev, Continuous – time branching processes with decreasing state dependent immigration, Advances in Applied . Probability, 16, 1984, 697-714.
(paper [1], 1978)
[26] K.V.Mitov, N.M.Yanev, Critical branching processes with decreasing state dependent immigration, C.R. de l’Acad. Bul. Sci., 36(2), 82.
(To the paper [1], 1978)
[27] N.M.Yanev, K.V.Mitov, Branching processes with decreasing migration, C.R. de l’Acad. Bul. Sci. 37(4) , 83.
(paper [1], 1978)
[28] N.M.Yanev, K.V.Mitov, A critical branching process with decreasing migration., Serdica – Bul. Math. Journal, Vol.11, 1985, p. 240-244
( paper [1], 1978)
[30] K.V.Mitov, N.M.Yanev. Vetvjashchiesja processi s ubivajushchej immigraciej zavisjashchej ot sostojanija processa. Serdica – Bul.Math.Journal.,Vol.11, 1985, 25-41.
(paper [1], 1978)
[31] K.V.Mitov, The maximal number of particles in a branching process with state-dependent immigration. Proc. Of VIII Summer School on Prob. And Statist., Sozopol, Bulgaria, 1997.
( paper [2], 1997)
[32] Yanev G.P. and Yanev N. M.. Branching processes with two types emigration and state dependent immigration, Athens Conference on Applied Probability and Time Series, 1996 – math.usf.edu.
( monograph [1])
[33] Arsenjev B. D., Ivanov V. M., Kulchitskiy. Adaptive Methods of Computing Mathematics and Mechanics, World Scientific, Ser. Mathematics, 1999.
( monograph [1])
[34] Mitov, K. V., The maximal Number of Particles in a Branching Process with State-Dependent Immigration. Pliska Studia Mathematica Bulgarica, 13(2000), 161-167.
( Preprint [3], 1996)
[35] Yanev, G. P. and Yanev, N. M. Limit Theorems for Branching Processes with Random Migration Components. Pliska Studia Mathematica Bulgarica, 13(2000), 199-205.
(books [1] and [2])
[36] Yanev G. P., Tsokos Ch. Family size order statistics in Branching Processes with immigration, Stochastic Anal. Appl., 18, (2000), No 4, P. 655-670.
( paper [2], 1997)
[37] Nevzorov V. B. “Records: Mathematical Theory” Translations of Mathematical Monographs, V. 194. , 2001
(paper [1], 1996 (IMA volumes, v.84) and to the Proceedings of Second International Workshop in Stochastic Modeling , 1996 [1])
[38] Roos B., Pfeifer D. “On the distance between the distributions of random sums, Journal of Applied Probability, V. 40, No. 1, 2003, P. 87-107,
( Monograph [1], 1995)
[39] K.V. Mitov, A. G. Pakes, G. P. Yanev. Extreme of geometric variables with applications to branching processes. Statistics and Probability Letters, 2003, 65, No. 4, P. 379-388.
( paper [1], 1999 and [1] in Proceedings of WCNA, Athens 1997)
[40] Yanev G., Mitov K. Maximum individual score in critical two-type branching processes, C.R. Acad. Bulg. Sci. 55, 2002, No 11, P. 17-22
( paper [1], 1999 and [1] in Proceedings of WCNA, Athens 1997)
[41] Yanev G. P., Mitov K. V., Yanev N. M. Critical branching regenerative processes with migration, Journal of Applied Statistical Science, 2003, 12, No. 1, P. 41-54.
( Monograph [1], 1995 and paper [3], 2000)
[42] Frenkel S. L. Random Summation and its Applications in Performance Modelling of Computer Systems, Proceedings of 17 th European Simulation Multiconference, June 2003, Nottingham UK, P. 278-284.
( monograph [1], 1995)
[43] Ahsanullah M. Record Values-Theory and Applications, University Press of America, Inc. , 2004.
(papers [3], 1995 ,C7 , [2], 2001, C5, [3], 2003, C5)
[44] Hasan H., Kharuiddin A. F. Exceedance problems for critical branching processes, Proceedings of “Simposium Kebangsaan Sains Matematik ke-XIII, May-June, 2005.
(monograph [1], papers [2] and [3], 1998)
[45] N. Lalam and C. Jacob Estimation of the offspring mean in a supercritical or near-critical size-dependent branching process
Source: Adv. in Appl. Probab. 36 (2004), no. 2, 582–601.
( monograph [1], 1995)
[46] Lalam, N. and Jacob, C. (2002). Estimation of the offspring mean in a supercritical or near-critical size-dependent branching process. Tech. Rep., Applied Mathematics and Informatics, INRA, Jouy-en-Josas.
( monograph [1], 1995)
[47] Lalam, Nadia; Jacob, Christine Estimation of the offspring mean of a supercritical or near-critical size-dependent branching process. C. R. Math. Acad. Sci. Paris 339 (2004), no. 9, 663--666. (Reviewer: Inés Maria del Puerto) 62M05 (60J80)
( monograph [1], 1995)
[48] Dorman, Karin S.; Sinsheimer, Janet S.; Lange, Kenneth In the garden of branching processes. SIAM Rev. 46 (2004), no. 2, 202--229
( monograph [1], 1995)
[49] Yanev G. P., Yanev N. A critical Branching Process with Stationary-Limiting Distribution, Stochastic Anal. Appl., 2004, V. 22, No 3, 721-738
( monograph [1], 1995 and paper [3]. 2000)
[50] ] Lalam, Nadia; Jacob, Christine. Estimation of the offspring mean for a general class size-dependent branching process. Applications to quantitive polymerase chain reaction. Mathematics and Computer Science III, 539-540. Trends Math., Birkhauser, Basel, 2004.
( monograph [1])
[51] Silvestrov D. S. Limit Theorems for Randomly Stopped Stochastic Processes. Springer, Ser. Probability and Its Applications, 2004.
( paper [1], 1987 and monograph [1])
[52] JACOB, C., LALAM, N. Estimation of the Offspring Mean in a General Single-Type Size-Dependent Branching Process, Pliska Stud. Math. Bulgar. V. 16, 2004, 65–88
( monograph [1])
[53] Yanev G. P. Revisiting offspring maxima in branching processes, Pliska Stud. Math. Bulgar. 18, 2007, 401-426.
( paper [1], 1999 and [1] in Proceedings of WCNA, Athens 1997)
[54] C Magnus, G Alsmeyer Mathematische Modellierung und Analyse der Polymerase-Kettenreaktion, - wwwmath1.uni-muenster.de
( monograph [1])
[55] Ispany M. Limit theorems for normalized nearly critical branching processes with immigration, Publ. Math. Debrecen, 2007, No 3340.
( monograph [1])
[56] Lalam, N. and Jacob, C. Estimation of the offspring mean of a supercritical or near-critical size-dependent branching process. Computes Rendus Mathematique, V. 339, 2004, No 9, P. 663-666.
(monograph [1])
[57] Ispány, M.(H-LAJOIF); Pap, G.(H-LAJOIF); van Zuijlen, M. C. A.(NL-RUNJ) Critical branching mechanisms with immigration and Ornstein-Uhlenbeck type diffusions. Acta Sci. Math. (Szeged) 71 (2005), no. 3-4, 821--850
( monograph [1] and Paper [1], 1984)
[58] Silvestrov D.S. Convergence in Skorokhod J-topology for compositions of stochastic processes, Theory of Stochastic Processes, Vol 14 (30), No 1, 2008, P. 126-143.
( monograph [1])
D.
PROFESSIONAL ACTIVITIES
D1. Editorship in Mathematical Journals
Associate editor of the "Journal of Applied Statistical
Science"
( USA, 1994- ).
Associate editor of “Pakistan
Journal of Statistics” (1996-)
Associate editor of the journal “Istatistik” (Turkey, 1996-)
Referee of “Journal of Applied
Probability” (England, 1996-)
Referee of “ Advances in Applied
Probability” (England, 1996-)
Reviewer of “Mathematical
Reviews” of American Math.
Society (April 1981 - present)
D2. Awards and
scholarships
1. A Silver medal for achievements and excellent
results in study, Fergana , USSR
2. Romanovski Award for
the best scientific results by yang researchers, USSR
3. A grant from ISI Tokyo Session Memorial Program
to participate at 51st ISI Session. The Institute of
Statistical Research, Tokyo ,
Japan
I never had a scholarship since the education
in my country used to be free.
D3. Conference
Organization
1.1 ST World Congress of Bernoulli Society. V.1,
Member of the National Organizing Committee.
2. 51 ST Session of the
International Statistical Institute,
Organizer
of the
meeting of invited papers “Population
Dynamics with Migration
Effects”.
3. International
Conference on Statistical Sciences,
D4. Consulting
[1] Chairman, Supervision
Committee;
[2] Consultant of State Statistical
D5. Involvement in Thesis Supervision
.
On involvement in
supervision of PhD and Master theses please see part B3 of the CV.
D6. Examination of Theses
1.
Member
of The Research Council of Romanovski
Mathematical
Each year 10 to 15 theses were considered .
2.
Referee of a PhD Thesis by A. Smadi on Time Series. Department of Statistics,
3.
As a statistician I am participating in evaluation of research works for promotion to Associate and Full Professor ranks in overseas
universities. The last year I was asked by the Temple University (USA) to
evaluate one candidate for promotion to the rank of Full Professor.
D8.
Refereeing Papers in Journals
Refereeing and reviewing 8 - 10 research articles a year for variety
of conference proceedings and journals, including 4 international journals such
as “Journal of Applied Probability” and “Advances in Applied Probability” (
D9.
Public Seminars and Presentations
1.
From
1978 to 1993 I have given one or two
seminars a year at Romanovski Mathematical Institute
of Uzbek Academy of Sciences.
During
those years I have
also given at least one seminar a year at
2.
In 1984 and 1989-1991 I have given one seminar
a year at Steklov Mathematical Institute of Academy
of Sciences of The USSR.
In 1990 I gave a seminar at
In 1991 I gave a seminar at
3.
From 1993 to 1995 I have given one seminar a
year at
In 1993 gave seminars at Khojitepa
and Gazi universities,
5.
In June of 1994 I gave a seminar on Record
Values at
6.
In 1996 I gave a series of seminars at
In 1996 I gave a seminar at
In 1997 I gave a seminar at University Kebangsaan,
7.
In 1998 I gave a seminar on “Effect of
Migration in Stochastic Population Processes”
at KFUPM, Dhahran.
8.
On
9. On
10.
On
11.
On
12.
Short Course "Stochastic Integration" ,
April-May, 2002, Department of Mathematical Sciences, KFUPM, Dhahran.
13.On
14.On
15. On
at KFUPM, Dhahran.
D10.
Presentations in Conferences and Workshops
[1] Stochastic Processes, a 6 hours Workshop at UKM, August, 1997,
[2] The Effect of
Migration in Population Dynamics, A presentation at UKM, August,
1997,
[3] A series of Lectures " The
Statistical World of Atoms" for graduate students of the Department of
Physics, May 2005, KFUPM, Dhahran.
E.
UNIVERSITY AND PUBLIC SERVICES
[1] Associate Editor of
“Proceedings of Romanovski Mathematical Institute on
Probability and
Statistics”,
[2] Responsible Secretary for Center for Stochastic Processes,
[3] Member of The Scientific
Committee of Romanovski Mathematical Institute for
conferring Ph.D and Doctor of Science Degrees.
[4] In charge of visits by prospective
students
1993-1996
[5] Organizer and Supervisor of the
Weekly Seminar on Stochastic Processes ( School of Mathematical Sciences, USM).
The mission of the seminar was:
(a) Discussion of Scientific results concerning research activity of
faculty members
(b) Work with the literature of joint interest;
(c) Discussion of current results and degree
thesis of graduate students in order to assist
them
to finish it in time.
1996-1998
[6] Organizer of the meeting of invited papers “Population Dynamics with
Migration
Effects” at 51 ST
Session of the International Statistical Institute,
[7] Involved in the development of the proposed BS program with Stochastic
processes and Time Series Analysis at the Department of Mathematical
Sciences, KFUP,
[8] Serving as a member of
Search Committee at the Department of Mathematical Sciences,
KFUPM,
[9] Served as a member of Ad-hoc Committee to evaluate promotion requests of
some candidates at the Department of Mathematical Sciences, KFUPM,
[10]
Served as a member of Research ,
Colloquia and Publications Committee member at the Department of Mathematical
Sciences , KFUPM,
[11]
Served as a member of Ad-hoc Committee to review the
current graduate program at the Department of Mathematical Sciences, KFUPM,
[12] Serving as a member of the University Research Advisory
Committee 2006-now