The history of the Kiev school of probability theory begins in the middle of the nineteenth century. The first lecture of this mathematical discipline was given at the Kiev University of St. Vladimir in 1863 by M.Ye. Vaschenko-Zakharchenko (1825-1912) for admission to the post of assistant professor. In Ukraine the first textbook on probability theory was published in 1878 by his disciple and colleague Professor V.P. Yermakov (1845-1922). At that time it was one of the most up-to-date textbooks, in particular it taught the new results of the law of large numbers by P.L. Chebyshov, a Russian mathematician. In 1898 V.P.Yermakov became the first Head of Department of Higher Mathematics of the KPI. In 1905 V.P.Yermakov published the reference guide "Least square method", which contributed to the widespread usage of the described probabilistic tool in many fields of science.
Professor of Kiev University D.O. Hrave (1863-1939), along with the scientists of Stockholm University (F. Lundberg, G. Kramer) was a pioneer in the creation and development of actuarial mathematics. He published textbooks "Insurance mathematics" (1912), "Theory of pension funds" (1917), "Mathematics of Social Insurance" (1924).
Since 1908 D.O. Hrave started to conduct his famous seminars, where a pleiad of prominent mathematicians was brought up, among them was the world-known Ukrainian mathematician M.P. Kravchuk (1892-1942).
In 1934 D.O.Hrave was one of the founders and the first director of the Institute of Mathematics of the NAS of Ukraine, which included the former Departments of Natural and Technical divisions of the NAS of Ukraine: Applied Mathematics (Head D.O. Hrave), Pure Mathematics (H.F. Pfeyffer) and Mathematical Statistics (M.P. Kravchuk).
Being the chairman of the Mathematics Department of the KPI, in the late twenties – early thirties M.P. Kravchuk cultivated probability-theoretical and statistical researches. Together with his disciples O.S. Smohorzhevsky, K.Y. Latysheva and S.M. Kulik, he studied orthogonal polynomials, correspondingly to certain probable classifications. In the world literature now the polynomials, generated by Bernoulli distribution, are called Kravchuk polynomials.
In the KPI the research of M. Kravchuk was later continued by professor A.S. Smohorzhevsky (1896-1969), who developed and distributed his ideas in the walls of university in the war and postwar years until the 1960s. He authored works, accordant with the ideas of his teacher, such as "On unitary and orthogonal transformations" (1931), "On orthogonal polynomials, connected with S.N. Bernstein probabilistic scheme" (1936).
At that time appeared the classic works by M.N. Krylov and his disciple M.M. Boholubov about the ergodic theory of Markov chains with unrestricted phase-space. The post-graduate student of M.M. Boholubov Y.I. Hikhman worked on the study of dynamic forces under random forces and justification boundary transition of systems in 1939-1941.
An outstanding contributions to the Ukrainian, in particular, Kyiv School of probability theory, were made by B.V. Hnedenko – in 1930-s he was a post-graduate student of the Moscow State University, a disciple of O.Y. Khinchyn and A.M. Kolmohorov. In the academic year 1944/1945, he gave a short course of probability theory in Kiev and conducted the student’s seminar "Fourier transform in probability theory and analysis". His first disciples were Ju.P. Kholodtsi, I.D. Kvit, K.L. Rvacheva (Yushchenko), D.H. Meyzler, O.S. Parasyuk, B.N.Harshteyn and others. In 1948 B.V. Hnedenko was elected an academician of the USSR Academy of Sciences and headed both the Probability theory Department at the Institute of Mathematics and the Probability Theory subdepartment at the Kiev State University (KNU).
Under his research management, the original and descriptive method for solving combinatorial problems, so-called "the trajectories method", was developed in the works of KNU students V.S. Korolyuk, V.S. Mykhalevych, B.I. Yaroshevsky, Kh.L. Berlyand. Eventually, while preparing the second edition of his unique book "Probability Theory and Its Applications", an American mathematician V. Feller included a special section on the trajectories method, where the results of B.V. Hnedenko and his students were presented.
Under the influence of B.V. Hnedenko, A.V. Skorokhod (1930-2011) started his brilliant scientific career. His role in the development of the Ukrainian school of probability theory can be hardly overestimated. Since 1964 he headed the Theory of random processes Departament at the Institute of Mathematics of the NAS of Ukraine, gave basic and special courses "Processes with independent increments", "Markov Processes", "Stochastic differential equations", "Random Operators" and others, superintended the work of a scientific workshop and numerous post-graduate students, wrote many monographs, among which are "Studies of stochastic processes" (1961), "Stochastic processes with independent increments" (1964), "The theory of stochastic processes," in 3 vols. (1971-1975). In 1964 A. Skorokhod and Y.I. Hikhman completed the first textbook on theory of stochastic processes in the Soviet Union, called "Introduction to the theory of stochastic processes".
Due to the initiative of B.V. Hnedenko, a specialization "Probability Theory and Mathematical Statistics" was founded at the Departament of Mechanics and mathematics at the KNU early in the year 1958. Students of mathematics, who specialized in probability theory, listened to required studies such as "Related Topics probability theory", "Theory of Stochastic Processes", "Mathematical Statistics", instead of studying methodical disciplines. In 1962 a separate department of probability theory and mathematical statistics was founded, the head of which was Professor Y.I. Hikhman. In 1966 the department was headed by his disciple – Doctor of Physical and Mathematical Sciences, Professor, Corresponding Member of the NAS of Ukraine, M.I. Yadrenko (1932-2004), a laureate of the State Prize of Ukraine in Science and Technology. He has founded the school of the theory of random fields and processes in Kyiv, which is known worldwide. M.Y. Yadrenko created a new trend in probability theory – spectral theory of homogeneous and isotropic random fields. For a series of papers on the theory of random fields, he was awarded the Acad. M.M. Krylov Prize of the NAS of Ukraine (1993). His monography "Spectral theory of random fields" was translated into English and published in the USA (1983). Among his disciples were 45 Candidates of Physical and Mathematical Sciences, 10 of which have passed Doctor of Science defense.
In 1951, after graduating the Mechanics and Mathematics Departament of the KNU, Y.L. Daletskyy (1926–1997) came to work in the KPI. The main direction of his research was the evolutionary differential equations in infinite dimensional spaces. In those studies the methods of stochastic processes, functional analysis and differential geometry infinite dimensional manifolds were widely used. In the 1960s Y.L. Daletskyy began to develop a new direction –theory of stochastic equations in infinite-dimensional smooth manifolds. Together with A. Skorokhod, Y.L. Daletskyy ran the scientific workshop "Random processes and distributions in functional spaces" for many years.
One of B.V. Hnedenko disciples, I.M. Kovalenko, Doctor of Physical and Mathematical Sciences, Professor, Academician of the NAS of Ukraine, was the first dean of the Applied mathematics Department in the 1990–1994 (as a volunteer), headed the department of the V.M. Hlushkov Institute of Cybernetics of the NAS of Ukraine for a while. His monographs significantly developed queuing theory, in mathematical theory of reliability, probabilistic combinatorics with the application of cryptography and stochastic geometry.
V.V. Buldyhin (1946-2012) graduated a KNU specialization, founded by B.V. Hnedenko in 1970. He is one of the best representatives of the KPI School of Probability Theory, also V.V. Buldyhin is a world-known Doctor of Physical and Mathematical Sciences, Professor, laureate of the State Prize of Ukraine. From 1974 to 1986 he worked at the Theory of random processes Department at the Institute of Mathematics of the Academy of Sciences of the USSR, the head of which at that time was A.V. Skorokhod.
In 1986 V.V.Buldyhin chaired the Subdepartment of Advanced Mathematics #1 in KPI, which in 1996 was transformed into the Department of Mathematical analysis and probability theory. V.V. Buldyhin obtained important results in the theory of random series in topological vector spaces, the theory of limit theorems for random vectors, the theory of Gaussian and sub-Gaussian processes, statistics, stochastic processes, renewal theory. Professionals know his monographs "Convergence of stochastic elements in topological spaces", "Brunn–Minkowski inequality and its Applications" (together with A.B. Kharazishvili), "Functional methods in problems of summation of random variables" and "Asymptotic Behavior Linearly Transformed Sums of Random Variables" (together with S.O. Solntsev), "Metric characteristics of random variables and processes" (together with Y.V. Kozachenko).
His disciples, including 13 Candidates and 3 Doctors of Physical and Mathematical Sciences, are now sharing their experience and knowledge in order to develop probability theory, both in Ukraine and abroad.
For many years together with V.V. Buldyhin such professor as O.I. Klesov, O.V. Ivanov, A.Y. Pylypenko, assistant professor A.B. Ilienko worked fruitfully in the KPI, developing the direction of probability theory. In 2012, after the death of V.V. Buldyhin, the department was headed by Doctor of Science, professor. O.I. Klesov – a former postgraduate of M.I. Yadrenko. O.I. Klesov retained and supported the team of young scientists, whose master's theses superwiser and reviewer was V.V. Buldyhin. He makes efforts to preserve the history and traditions of the Department, to gain its credibility among the scientific institutions of the country and the whole world.
