A Guide to the Russian Academy of Sciences - University of Texas ...

Kolmogorov); 2. Asymptotic methods of Probability Theory and Statistics (A. Ya.
Khinchin, A. N. Kolmogorov, N. V. Smirnov, Iurii V. Prokhorov, D. M.
Chibisov, V. V. Sazonov, and V. M. Zolotarev); 3. Theory of random processes
and fields, including information theory (A. Ya. Khinchin, and A. N.
Kolmogorov), purely iump processes (A. Ya. Khinchin, and B. A. Sevast'yanov),
foundations of statistical mechanics and quantum statistics (A. Ya. Khinchin and
later A. S. Holevo), stationary processes and fields (A. N. Kolmogorov, Iurii A.
Ozanov, for more details see the section on Laboratory of stochastic processes and
fields), stochastic control (A. N. Kolmogorov, and A. N. Shiryaev, for more
details see the section on Laboratory of statistics of stochastic processes), branching
processes.
The theory of branching processes, which originated in the 1940s in A. N. Kolmogorov's
school, was subsequently developed by B. A. Sevast'yanov and his students and
followers V. P. Chistyakov, V. F. Kolchin, A. M. Zubkov, V. A. Vatutin. From
the middle of the 1960s, active investigation of a number of probability problems in
discrete mathematics (random all locations of particles, random maps, random
graphs, distribution of s-tuples in random sequences etc.) were carried out by B. A.
Sevast'yanov, V. P. Chistyakov, V. F. Kolchin, A. M. Zubkov, V. G. Mikhailov.
In Statistics, the main directions of theoretical research were nonparametric
methods, properties of order statistics, asymptotic theory of different tests (N. V.
Smirnov, A. N. Kolmogorov, L. N. Bol'shev, N. N. Chentsov, and D. M.
Chibisov).
14. Laboratory of Statistics of Stochastic Processes of the Department of
Probability Theory and Mathematical Statistics: The staff of the
Laboratory of Statistics of Stochastic Processes are: A. N. Shiryaev (Head of
Laboratory), A. A. Novikov, A. V. Mel'nikov, D. D. Kramkov.
In 1957-1960, members of the Steklov Mathematical Institute V. P. Leonov and A. N.
Shiryaev, under supervision of A. N. Kolmogorov (in connection with some
nonlinear problems of the theory of stochastic processes and needs of
radiotechnics) developed a technique of handling moments and semi-invariants of
high orders. This technique is applicable to many problems in nonlinear analysis
and nonlinear transformations of stochastic processes, as well as to proofs of limit
theorems of probability theory.
In 1959, A. N. Kolmogorov and A. N. Shiryaev started research (originated from
problems in radio location) devoted to the development of methods of fastest
detection of changes of characteristics of observed data (``the change point
problem''). Not only the problems suggested by radio engineers were solved, but a
large scale investigation of optimal stopping rules was initiated, which was
fundamental for the optimal stochastic control and was summed up in A. N.
Shiryaev's monograph ``Statistical sequential analysis''.
``The change point problem'' revealed the importance of investigation of problems of
optimal nonlinear filtration. A detailed exposition of the relevant theory and its
applications is given in R. S. Liptser and A. N. Shiryaev's monograph ``Statistics
of stochastic processes''.
In subsequent years A. N. Shiryaev jointly with his students and colleagues (in particular
A. V. Mel'nikov and A. A. Novikov from the Laboratory) systematically studied
stochastic processes of martingale types. Martingales, semi-martingales and related
stochastic calculus, together with stationary and Markov processes, constitute one
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