The Department was founded in 1938.

The following scientists headed the Department of Probability Theory and Mathematical Statistics:

1. Academician V.I. ROMANOVSKY. Period of leadership: 1938-1954;
2. Academician T.A. SARIMSAKOV. Period of leadership: 1954-1958;
3. Academician S.Kh. SIROJIDDINOV. Period of leadership: 1958-1988;
4. Academician Sh.K. FORMANOV. Period of leadership: 1990-1995;
5. Academician T.A. AZLAROV. Period of leadership: 1995-2005;
6. Professor A.A. Abdushukurov. Period of leadership: 2006-2017;
7. Professor O.Sh.Sharipov. Period of leadership: 2018-present.

The National University of Uzbekistan became the place of birth of the world-famous scientific school in probability theory and mathematical statistics in Uzbekistan. Theoretical and applied research in this field of mathematics began with the establishment of the university, which was founded by the outstanding mathematician Vsevolod Ivanovich Romanovsky.

Academician V.I.ROMANOVSKY

(1879-1954)
All the achievements of Uzbek scientists in recent times have become associated with the name of this great person. As a brilliant scientist and an outstanding educator, he found many talented pupils in Uzbekistan and made a tremendous contribution to helping them find their place in the field of mathematics. V.I. Romanovskiy’s principal research was in the areas of theoretical and applied mathematical statistics, which is well known to contemporary mathematicians. His most renowned work that brought him international recognition was the study of distribution functions of empirical characteristics. It is worth particularly noting V.I. Romanovskiy’s research on finite Markov chains. Before the Second World War, his monographs Mathematical Statistics (1938), Issledovaniya po sepyam Markova (1939, in French), and Elementary Course of Mathematical Statistics (1939) attracted the attention of mathematicians around the world. After the 1940s, V.I. Romanovskiy focused on systematizing his conclusions on Markov chains (including Bruns chains, multi-state Markov chains, bicyclic chains, etc.). The scientist proved various limit theorems in this area. During this period, as a mentor he was also involved in practical statistics problems, publishing Primenenie matematicheskoy statistiki v opytnom dele (1947), Diskretnye tsepi Markova (1949), and Osnovnye zadachi teorii oshibok (1947). In total, V.I. Romanovskiy left behind more than 200 scientific articles and monographs. This legacy now forms the golden fund of modern Uzbek mathematics. Several of his monographs were repeatedly published in Uzbek, Russian, French, and English in Uzbekistan and abroad.
V.I. Romanovsky was also awarded state awards. After independence, his services were highly appreciated by our government and President, and in 2004 he was awarded the Order “For Great Services”.

Academician T.A.SARIMSAQOV

(1915-1995)
The famous academic scientist Toshmuhammad Alievich Sarimsoqov (1915–1995) began his career in the scientific school of V.I. Romanovskiy, and his early research was connected with applying methods of probability theory to classical analysis. A number of his works on Markov chains also attracted the attention of mathematicians worldwide. He extended the matrix method introduced by V.I. Romanovskiy to both finite Markov chains and Markov chains with a continuous state space, conducting in-depth research in this area. As a result of these studies, in 1954 he published the monograph Osnovy teorii protsessov Markova in Moscow. Additionally, the scientist devoted attention to applying Markov chains in regions of Central and Inner Asia, and for several articles and works on this topic he was awarded multiple State prizes.
In the 1960s a new era began in T.A. Sarimsoqov’s work. He started working on topological semifields, their topology, and the application of these concepts to functional analysis and probability theory. Based on these studies, T.A. Sarimsoqov trained many students and founded another very famous mathematical school in Uzbekistan in these fields.

Academician S.Kh.SIROJIDDINOV

(1920-1988)
Another great scientist who expanded V.I. Romanovskiy’s scientific school into a new direction and created his own scientific school was Sa’di Hasanovich Sirojiddinov (1920–1988). He established his own school in probability theory and mathematical statistics and rose to worldwide prominence in these fields. At the end of the 1940s, under the guidance of V.I. Romanovskiy, he studied multivariate polynomials and Hermite polynomials. The limit theorems for homogeneous Markov chains proved by S.H. Sirojiddinov became known in the mathematical world. Continuing the work of A.N. Kolmogorov, he was able to obtain precise estimates for limit theorems for sums of random variables that form Markov chains. He established asymptotic expansions in both one-dimensional and multivariate theorems. The results of these investigations quickly elevated S.H. Sirojiddinov to the status of a leading specialist. Later, S.H. Sirojiddinov continued his research on Markov chains in collaboration with his students, achieving a number of generalized results. Together with his pupil Sh.Q. Farmonov he co-authored the monographs Predel’nye teoremy dlya odnorodnykh tsepey Markova (1955) and Predel’nye teoremy dlya summ sluchaynykh vektorov, svyazannykh v tsep Markova (1979). These works were recognized by experts and later further developed by mathematicians in Moscow, Vilnius, and Tashkent. S.H. Sirojiddinov’s students also followed in his footsteps, obtaining many mathematical results in limit theorems, additive problems, statistical acceptance control, and other areas, achieving results acknowledged around the world.

Academician T.A.AZLAROV

(1938-2011)
Tursun Abdurahimovich Azlarov is a leading scientist in our country in the fields of probability theory and mathematical statistics. His achievements in the modern and promising directions of this field are well known to specialists and have been recognized by them. T.A. Azlarov earned the degree of Doctor of Physical-Mathematical Sciences in 1973, became a professor in 1974, was elected a corresponding member of the Republic’s Academy of Sciences in 1979 and a full member (academician) in 2000. He was a laureate of the State Prize named after Abu Raykhon Beruni in 1973. He authored more than 150 scientific articles, of which around 40 were published in foreign journals.
His monograph “Problems of Characterization Related to Indexed Distributions” was translated into English and published by the renowned German publisher Springer in 1986. Under his supervision, 34 candidates of science were trained, among whom two went on to become doctors of science.
T.A. Azlarov made significant contributions to the mathematical theory of queuing systems, to limit theorems in probability theory, to characterization problems in distribution theory, to the asymptotic theory of statistical criteria for homogeneous Markov chains, to limit theorems for sums of random variables with random counts, including the estimation of their rates of convergence and asymptotic expansions, and to the theory of approximation of continuous functions.
He combined his highly productive scientific work with effective pedagogical-methodological and public activities. His original two-volume textbook on mathematical analysis (in collaboration with X.T. Mansurov), whose second edition was published in 1995–96, made a significant contribution to training mathematical specialists. A two-volume mathematics manual published under his direct participation and editorial guidance has for many years served as a daily reference book for school teachers.
T.A. Azlarov always pursued his scientific research alongside training qualified scientific and pedagogical personnel and promoting the science. He traveled to Hungary (1969–1974), Japan (1972), Poland (1976), Bulgaria (1978), India (1982, 1983), Sweden (1988), Egypt (1996) and other countries where he was invited to deliver lectures and successfully participated with scientific presentations at international conferences.

Academician Sh.Q.FARMONOV

Shokir Qosimovich Farmonov is a beloved and respected disciple of the great academic scientist S.H. Sirojiddinov. He has made significant and ongoing contributions to the development of probability theory, mathematical statistics, and their applications. Farmonov continued his mentor’s research on the theory of Markov chains, extending it by studying homogeneous multivariate Markov chains with arbitrary state spaces, thus advancing this area of theory to a new level.
Sh.Q. Farmonov is recognized internationally as a specialist in one of the main modern directions of mathematics — probability theory and mathematical statistics. His scientific and pedagogical activities are closely connected with Mirzo Ulugbek National University (formerly Tashkent State University), where he serves as a professor in the Department of Probability Theory and Mathematical Statistics.
Farmonov earned his Doctor of Physical and Mathematical Sciences degree in 1973 and became a professor in 1977. He was elected a corresponding member of the Academy of Sciences of the Republic of Uzbekistan in 1994 and a full member (academician) in 2000. In 1973, he was awarded the State Prize of Uzbekistan named after Abu Raykhon Beruni for his work on limit theorems in probability theory and their applications.
He has presented the results of his scientific research at international scientific centers in countries such as Russia, the United States, Japan, Ukraine, Lithuania, Hungary, Poland, Malaysia, and Mongolia, and at international conferences in France, Sweden, Singapore, and other nations.
Alongside his productive scientific work, Sh.Q. Farmonov has always focused on training scientific and pedagogical personnel. To date, more than 30 candidates of science (Ph.D. equivalents) and over 10 doctors of science have been trained under his supervision. In addition to Mirzo Ulugbek National University, he has delivered lectures at many higher education institutions and teacher training institutes across the country, and has actively participated in organizing and conducting mathematics olympiads at all levels.
In recent years, Sh.Q. Farmonov has led the school of probability theory and mathematical statistics in Uzbekistan and actively collaborated with specialists from abroad. He regularly participates in conferences and forums, sharing new ideas and methods that support the continued development of this scientific field in Uzbekistan. 

Professor A.A. Abdushukurov

A.A. Abdushukurov is an expert in the field of the statistics of incomplete samples. His main scientific research focuses on nonparametric statistical estimation problems for incomplete observations. He has developed and studied nonparametric estimators for general models of incomplete samples. He is also a co-author of the celebrated ACL (Abdushukurov–Cheng–Lin) estimator, which appears in statistical literature in the context of survival function estimation under censoring models and has important asymptotic properties.
Using basis functionals, he constructed nonparametric estimators for generalized models of incomplete observations, and he completely analyzed their asymptotic properties, including strong consistency, convergence rates, and Gaussian approximation results. His work in this area has significantly advanced the theory of nonparametric statistics for censored and incomplete data.
Under his supervision, 20 master’s theses and 5 candidate (PhD-equivalent) dissertations were defended. He is the author of more than 160 scientific and educational-methodological works.
His 2009 monograph “Statistics of Incomplete Observations” was recognized for its contribution to the field, and in 2010 won a competition for “Best Textbook and Educational Literature” established by the Talent Foundation. Another textbook “Probability Theory and Mathematical Statistics” (2011) also received this award.
In 2011, the following three monographs were published by LAM­BERT Academic Publishing:
Nonparametric Estimates of Functionals from Unknown Distributions Based on Incomplete Observations and Their Statistical Analysis: 1.Estimation of Multivariate Distributions and Their Mixtures from Incomplete Data (co-authored with R.S. Muradov) 2.Asymptotic Analysis of Kernel Estimates Related to the Mean (co-authored with K.S. Sagidullaev). 3.In 2011 he also contributed as a co-author to the “International Encyclopedia of Statistics” (Springer, USA), a 1700-page international statistical reference, collaborating with over 600 scientists from around 120 countries.

Professor O.Sh. Sharipov

Olimjon Shukurovich Sharipov is one of the leading specialists in the field of probability theory and mathematical statistics in the Republic of Uzbekistan. His scientific work is dedicated to limit theorems for random variables taking values in Banach and other infinite-dimensional spaces and their applications in mathematical statistics, including central limit theorems, laws of the iterated logarithm, invariance principles, and related results for weakly dependent random fields and processes.
Sharipov has published numerous research articles in these areas, addressing theoretical problems such as limit theorems for weakly dependent observations in Banach spaces and random fields, U-statistics, and related asymptotic properties.
He has over 200 scientific publications (including co-authored papers and monographs) and has participated in extensive international research collaborations and visits. He has been invited to give talks and work with colleagues at several leading universities abroad, including institutions in Germany (Göttingen, Kiel, Munich, Dresden, Bochum), Denmark (University of Copenhagen), Malaysia (University of Putra Malaysia), and Russia (Moscow State University), among others.
Professor Sharipov’s academic and research activities are closely tied to Mirzo Ulug‘bek National University (National University of Uzbekistan), where he serves as Head of the Department of Probability Theory and Mathematical Statistics. He holds the degree of Doctor of Sciences (DSc) and is a senior research scientist.
He is also a member of the Scientific Council that awards the Doctor of Sciences degree in physics and mathematics, and he has served on the Scientific-Technical Council for “Physics, Mathematics, and Mechanics” under the Ministry of Innovative Development of the Republic of Uzbekistan.
In editorial and professional service, Prof. Sharipov is on the editorial boards of journals such as the Uzbekistan Mathematics Journal, Bulletin of the Mathematics Institute, and the Malaysian Journal of Mathematical Sciences. He is also a member of international mathematical and statistical societies, including being part of the International Institute of Mathematical Statistics and the Bernoulli Society for Probability and Mathematical Statistics since the early 2000s.

The Department of Probability Theory and Mathematical Statistics regularly organizes the following international scientific conferences:

1. In cooperation with the V.I. Romanovskiy Institute of Mathematics of the Academy of Sciences of the Republic of Uzbekistan, Lomonosov Moscow State University, the Steklov Institute of Mathematics of the Russian Academy of Sciences, and the Faculty of Mathematics of National University of Uzbekistan named after Mirzo Ulugbek, the International Scientific Conference entitled “Limit Theorems of Probability Theory and Mathematical Statistics” was held on September 26–28, 2022.
2. In cooperation with the V.I. Romanovskiy Institute of Mathematics of the Academy of Sciences of the Republic of Uzbekistan, Universiti Putra Malaysia, Monash University Malaysia, International Islamic University Malaysia, National University of Malaysia, and the Faculty of Mathematics of National University of Uzbekistan named after Mirzo Ulugbek, the International Scientific Conference entitled “Stochastic Analysis” was held on October 21–23, 2024.