Scientific Laboratory of Stochastic Analysis
Laboratory Head
G‘anixo‘jayev Nosir Nabiyevich
Laboratory Head
📧 Email: nasirgani@yandex.ru
📞 Telefon: +99897 3946419
🕔 Reception days:
🏢 Office number: 217
📍 Address:
Address: 100174, Tashkent city, Almazar district, University street, house 4
More detailsAbout Laboratory
In 1943, the Institute of Mathematics of the Academy of Sciences of the Republic of Uzbekistan was established, and the Department of Mathematical Statistics and Probability Theory (headed by V.I. Romanovsky) was opened under it.
Laboratory staff actively participated in organizing the following conferences:
- In 1948, the Second All-Union Conference on Mathematical Statistics was held, attended by renowned scientists A.N. Kolmogorov, V.V. Gnedenko, and others.
- In 1962, in collaboration with the V.A. Steklov Mathematical Institute (MI) (Moscow) and Tashkent State University (TashSU) (now UzMU), the First Fergana Colloquium on "Limit Theorems of Probability Theory" was held (September 17-23, Fergana city).
- In 1967, a colloquium on "Mathematical Methods for Quality and Reliability Control of Products" was held with participation from Moscow State University and the V.A. Steklov Mathematical Institute (Moscow).
- In 1971, jointly with MI and TashSU, a colloquium dedicated to special problems in probability theory and mathematical statistics was organized.
- In 1972, the II Fergana Colloquium was organized together with MI and TashSU.
- In 1975, the III International Symposium on Probability Theory was held jointly with MI and Japan (Tashkent, August 26).
- In 1980, a Republican Conference on Probability Theory and Mathematical Statistics was organized.
- In 1983, in collaboration with MI and TashSU, the III Fergana Conference on "Probability Theory and Mathematical Statistics" was held.
- In 1986, the I World Congress of the Bernoulli International Society on Probability Theory and Mathematical Statistics was held.
- In 2000, a conference titled "Contemporary Problems in Probability Theory and Mathematical Statistics" was held dedicated to the 80th anniversary of Academician S.Kh. Sirojiddinov.
Between 1944 and 2021, the following distinguished scientists worked in the Department of Probability Theory and Mathematical Statistics: Academicians V.I. Romanovsky, T.A. Sarimsakov, S.Kh. Sirojiddinov, T.A. Azlarov, Sh.Q. Farmonov; Professors S.V. Nagaev, M.K. Kamolov, M.I. Eidelnat, T.L. Malevich, V.G. Vinokurov, A.V. Nagaev, B. Abdalimov, I.S. Badalbaev, I. Rakhimov, A. Starsev, Sh. Khoshimov, M.U. Gafurov, Sh. Mirakhmedov, O. Sharipov, and other renowned scholars. S.Kh. Sirojiddinov, a student of V.I. Romanovsky, was the institute's first graduate student. Later, he served for many years (1970-1983) as Vice President of the Academy of Sciences. He made a tremendous contribution to the development of mathematics in Uzbekistan.
Publications by Department Staff: [List of publications in Russian and Uzbek with authors, titles, and years - preserved as in original with titles like:
- V.I. Romanovsky's works on mathematical statistics (1947-1949)
- T.A. Sarimsakov's "Fundamentals of Markov Processes" (1954)
- Various textbooks and monographs through 2023]
The Department of Probability Theory and Mathematical Statistics was headed by: V.I. Romanovsky until 1949; S.Kh. Sirojiddinov in 1953-1954; M.I. Eidelnat in 1949-1953 and 1954-1960; R.Kh. Diveev in 1960-1967; V.G. Vinokurov in 1967-1972; T.A. Azlarov in 1972-1976; Sh.Q. Farmonov in 2001-2019. In 1976, based on the Department of Probability Theory and Mathematical Statistics, two departments were established: Probability Theory (headed by Sh.Q. Farmonov) and Mathematical Statistics (headed by T.A. Azlarov). The Probability Theory Department was headed by: Sh.Q. Farmonov in 1976-1990; I.S. Badalbaev in 1991-1995; Sh.Q. Farmonov in 1995-2001. The Mathematical Statistics Department was headed by: T.A. Azlarov in 1976-1980; S.Kh. Sirojiddinov in 1980-1983; M.U. Gafurov in 1983-1988; A.V. Nagaev in 1988-1994; Sh. Khashimov in 1994-2001. In 2020, the department was renamed "Stochastic Analysis." Between 2019-2023, Prof. Y.M. Khusanboev served as laboratory director. Currently (since 2023), the laboratory is headed by Prof. N.N. Ganikhodjaev.
In 1971, the institute's Probability Theory Department and Statistics Laboratories were merged to form the "Probability Theory and Mathematical Statistics" Department (headed by T.A. Azlarov).
State Awards Received by Department Staff:
- In 1973, S.Kh. Sirojiddinov, T.A. Azlarov, Sh.K. Farmonov, and M.M. Mamatov were awarded the Uzbekistan State Prize named after Beruni for their research in "Limit Theorems of Probability Theory and Their Applications."
- In 1977, young probabilists M.U. Gafurov, Sh.A. Mirakhmedov, Sh.A. Khoshimov, and Sh.A. Ismatullaev were awarded the Uzbekistan Prize for Young Scientists in Science and Technology.
Laboratory Staff
Scientific Activity
Laboratory staff conduct scientific research in the following areas:
-- Classical and non-classical variants of the central limit theorem for random sums;
-- Limit theorems for sequences of random variables and vectors;
-- Mathematical methods for statistical acceptance control of finished products;
-- Discrete problems in probability theory;
-- Boundary problems in probability theory;
-- Theory of asymptotic efficiency of statistical features;
-- Spacings-statistics and their applications;
-- Limit theorems and their applications for weakly dependent random variables taking values in finite and infinite-dimensional spaces: central limit theorem, law of iterated logarithm, enhanced law of large numbers, functional invariance principle;
-- Random fields: limit theorems for weakly dependent random fields taking values in finite and infinite-dimensional spaces, conditions of weak dependence for random fields;
-- Theory of U-statistics: limit theorems for U-statistics composed of independent and dependent observations;
-- Autoregressive processes: estimation of parameters of autoregressive processes, autoregressive processes with weakly dependent innovations, autoregressive processes in Banach spaces;
-- Bootstrap: bootstrap for U-statistics of weakly dependent observations;
-- Time series modeling;
-- Functional data analysis;
-- Moment and probability inequalities;
-- Construction of distribution functions (copula functions) of random vectors with given marginal distributions;
-- Asymptotics of sums of conditionally independent random variables;
-- Functional limit theorems for branching random processes with immigration;
-- Analysis of branching random processes in variable environments;
-- Monte Carlo method and its applications, mathematical models of decision-making under risk conditions;
-- Theory of limit Gibbs measures for lattice models of statistical physics;
-- Nonlinear dynamical systems and their applications;
-- Quadratic stochastic operators and processes;
-- Asymptotic theory of extreme order statistics;
-- Limit theorems for functionals of convex hulls;
-- Point process theory.
International Cooperation
The laboratory actively collaborates with numerous institutes and universities, including:
- V.A. Steklov Mathematical Institute (Moscow, Russia);
- Saint Petersburg Department of the V.A. Steklov Mathematical Institute;
- S.L. Sobolev Institute of Mathematics (Novosibirsk, Russia);
- M.V. Lomonosov Moscow State University (Moscow, Russia);
- Bochum University (Bochum, Germany);
- University of San Diego (California, USA);
- Taras Shevchenko National University of Kyiv (Kyiv, Ukraine);
- University of Copenhagen (Copenhagen, Denmark);
- Department of Statistics, USBE, Umeå University, Umeå, Sweden;
- Department of Statistics and Applied Probability, University of California, Santa Barbara, USA;
- Imperial College London (London, England);
- Stanford University (California, USA);
- Universiti Putra Malaysia (Kuala Lumpur, Malaysia);
- University of Magdeburg (Magdeburg, Germany);
- University of Debrecen (Debrecen, Hungary);
- Institute of Mathematics of the National Academy of Sciences of Ukraine (Kyiv, Ukraine).
Seminars
Modern and Urgent Problems of Probability Theory and Mathematical Statistics (scientific seminar)
Seminar venue: ZOOM ID- 9068141469
Every Wednesday at 10:00 at V.I.Romanovsky Institute of Mathematics, Room 105
Seminar leader: Prof. Y.M. Khusanboev, seminar secretary: S.O. Sharipov