Department of Probability Theory and Mathematical Statistics

From the time when the Department was organized in 1938 and until 1960, the Head of Department was A. N. Kolmogorov (excluding 1946–1948 when A. Ya. Khinchin occupied this position). From 1960 to 2013 the Department was headed by academician Yu. V. Prokhorov. During some period a part of the Department existed independently under the name Department of Mathematical Statistics successively headed by N. V. Smirnov, L. N. Bol'shev, D. M. Chibisov, and from 1983 to 1987 by A. N.  Kolmogorov.

In the 1940-s research in Probability Theory and in Statistics also was done outside the Department (S. N. Bernstein, O. V. Sarmanov). In the Department itself investigations in these fields were carried out by A. N. Kolmogorov, A. Ya. Khinchin, E. E. Slutsky, N. V. Smirnov. At the end of 40-s the Department was joined by B. A. Sevast'yanov and Yu. V. Prokhorov, and at the beginning of 50-s by L. N. Bol'shev. At that time a close assistant of A. N. Kolmogorov was A. A. Petrov. Special preparation to the degree of Doctor of Sciences had Yu. V. Prokhorov, V. S. Semenov, S. Kh. Sirazhdinov. Among graduate students at the Department were A. A. Borovkov, N. N. Chentsov, G. M. Maniya, and E. A. Nadaraya.

Along with theoretical research, great attention was paid to applications. Among them were

• theory of shell scattering (A. N. Kolmogorov);
• statistical quality control (A. N. Kolmogorov, S. A. Aivazyan, A. N.  Bol'shev, S. Kh. Sirazhdinov, I. A. Borodachev);
• composition of statistical tables (E. E. Slutskii, N. V. Smirnov, L. N. Bol'shev and their assistants E. S. Kedrova, V. F. Kotelnikova, M. A. Rybinskaya);
• queuing theory (A. Ya. Khinchin, Yu. V. Prokhorov, B. A. Sevast'yanov).

The main directions of theoretical research in the Department were:

• foundations of the probability theory (measure theoretic approach — A. N. Kolmogorov, V. V. Sazonov, Yu. V. Prokhorov, algorithmic complexity approach — A. N. Kolmogorov);
• asymptotic methods of probability and statistics (A. Ya. Khinchin, A. N. Kolmogorov, N. V. Smirnov, Yu. V. Prokhorov, V. M. Zolotarev, V. V. Sazonov, D. M. Chibisov);
• theory of random processes and fields (A. Ya. Khinchin, A. N. Kolmogorov, Yu. A. Rozanov), purely jump and branching processes (A. Ya. Khinchin, B. A. Sevast'yanov, V. F. Kolchin); statistical sequential analysis, stochastic calculus, martingales (A. N. Shiryaev, A. A. Novikov);
• foundations of statistical mechanics and quantum statistics, information theory (A. Ya. Khinchin, A. S. Holevo);
• nonparametric methods of mathematical statistics, properties of order statistics, asymptotic theory of different tests (N. V. Smirnov, A. N. Kolmogorov, L. N. Bol'shev, N. N. Chentsov, D. M. Chibisov).

Besides the mentioned above, at different times at the Department worked: K. A. Borovkov, B. I. Devyatov, M. P. Ershov, A. V. Kolchin, V. F. Kolchin, D. O. Kramkov, B. N. Leonov, V. K. Malinovsky, A. C. Miller, M. L. Nechaev, B. S. Stechkin, Yu. O. Usenko.

The goal of theory of probability and mathematical statistics is the study of the universal mathematical laws underlying the random phenomena, the development of methods for construction of mathematical models that reflect essential features of random data, application to the analysis of specific complex multicomponent systems in physics, engineering, computer science, economics, biology, social sciences. The modern trend in probability theory is also characterized by wide application of probabilistic methods in mathematical structures of diverse nature varying from geometry, algebra, representation theory and complex analysis to the theory of numbers, combinatorics and theory of algorithms. Currently the main directions of research in the Department of Probability Theory and Mathematical Statistics are:

• stochastic optimization and its application, including financial mathematics (A. N. Shiryaev, A. A. Gushchin, P. A. Yaskov, M. V. Zhitlukhin, A. A. Muravlev);
• non-commutative probability theory and its applications in quantum theory of information and statistical decisions (A. S. Holevo, M. E. Shirokov, G. G. Amosov);
• asymptotic methods in probability theory and statistics (O. V. Viskov, V. I. Khokhlov, D. M. Chibisov, A. L. Yakymiv).