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Mykhail Iosypovich Yadrenko

(16.04.1932-28.09.2004)

Professor Mykhailo Josypovych Yadrenko was a prominent mathematician and pedagogue, Corresponding Member of the Ukrainian National Academy of Sciences, Honored Personality of Science and Technology of Ukraine, and Doctor of Physical and Mathematical Sciences.

It is impossible to imagine the theory of random fields, one of the main branches of probability theory, without M. I. Yadrenko’s works, which founded numerous new directions of this theory. It is hard to overestimate his contribution to the development of mathematical education in the Ukraine and training of highly qualified mathematicians for the last 50 years.

M. I. Yadrenko was born on April 16, 1932 in the village of Drimailivka, Nizhyn district, Chernigiv region. In 1950-1955, he was a student of the Department of Mechanics and Mathematics at Kiev University, where he attended lectures of prominent mathematicians and teachers: N. N. Bogolyubov, B. V. Gnedenko, I. I. Gikhman. Under their guidance, M. I. Yadrenko began his scientific studies and published his first scientific work devoted to the investigation of properties of random walks.

In 1955-1958, he was a postgraduate student at the Kiev University. In those years, M. I. Yadrenko began his studies of homogeneous and isotropic random fields. These investigations were presented in his Candidate Degree Thesis.

After postgraduate courses, M. I. Yadrenko worked at the Department of Mathematical Analysis and Probability Theory at Kiev University. He devoted much energy to the development of mathematical education at secondary schools, organization of mathematical competitions, and publication of contemporary textbooks on elementary mathematics and combinatorial analysis and books of problems of mathematical competitions.

In 1966, M. I. Yadrenko became the Head of the Departmentof Probability Theory and Mathematical Statistics and headed it for more than 33 years. Under his guidance, the researchers of the department carried out investigations in the spectral theory of random fields (in particular, the Doctoral Degree Thesis of M. I. Yadrenko was devoted to this theory), asymptotic methods in probability theory, the theory of stochastic diferential equations, and applied problems in probability theory and mathematical statistics. The Department of Probability Theory and Mathematical Statistics was repeatedly distinguished as the best department of Kiev University.

In 1970 the “Teoriya Veroyatnostei i Matematicheskaya Statistika” journal (Probability Theory and Mathematical Statistics) was founded thanks to M. I. Yadrenko’s initiative (since 1992, this journal is published in Ukrainian). This journal has played an important role in the development of the world-renowned Kiev school in probability theory. Since 1974, the English version of this journal has been published by the American Mathematical Society. In 1969 M. I. Yadrenko founded another periodical edition, a collection of popular-science works “U Sviti Matematyky” (In the World of Mathematics). In 1995 “U Sviti Matematyky” was transformed into a popular scientific, methodical, and historical journal.This journal is intended for a broad circle of readers interested in mathematics from scholars to professional mathematicians.

As a scientist, M. I. Yadrenko is well known in the world for his works devoted to the theory of random fields and their statistical analysis. He is the author of more than 200 scientific works in this field, the majority of which were translated into English. A survey of the results obtained by M. I. Yadrenko in the theory of random fields can be found in the paper of V. V. Buldygin, Yu. V. Kozachenko, and N. N. Leonenko “On Yadrenko’s works in the theory of random fields” Ukr. Mat. Zh., 44, No. 11 (1992). One should especially note the M. I. Yadrenko’s monograph “Spectral Theory of Random Fields”, Vyshcha Shkola, Kiev (1980), which became a handbook for experts in random fields. This book was awarded the Prize of Ukrainian Ministry of Education, and its English version was published in 1983 in the USA.

M. I. Yadrenko devel opened the spectral theory of homogeneous and isotropic fields in Euclidean, Hilbert, and Lobachevskii spaces. These results were used by M. I. Yadrenko and his disciples for the solution of important problems of linear prediction and filtration of random fields. He founded the theory of Markov random fields – a new direction in the theory of random fields. Later, the theory of Markov random fields was further developed in works related to problems of statistical physics and quantum field theory.

M. I. Yadrenko obtained a series of important results related to the analytic properties of sampling functions of random fields. In particular, he established conditions for the continuity, analyticity, and quasi-analyticity of random fields. M. I. Yadrenko also investigated numerous important problems of statistics of random fields. For example, he established conditions for the absolute continuity and singularity of measures that correspond to Gaussian random fields and developed eficient methods for the solution of statistical problems for random fields (problems of extrapolation, filtration, interpolation, and estimation of regression coeficients).

M. I. Yadrenko obtained numerous important results in various branches of applied probability theory (optimal methods for quality control in mass production, statistical modeling of noises in semiconductors, statistical analysis of generators of random numbers, statistical problems of reliability theory, and statistical models of distributions with random intensity).

For a series of works in the theory of random fields, M. I. Yadrenko was awarded the Krylov Prize of the Ukrainian National Academy of Sciences.

M. I. Yadrenko is the founder and the leader of the well-known scientic school in random fields and processes. Among his disciples, there are 44 candidates of science. Twelve of his disciples became doctors of sciences; these are V. V. Anisimov, Corresponding Member of the National Academy of Sciences of Ukrainian, and professors V. L. Girko, Yu. V. Kozachenko, M. M. Leonenko, Yu. D. Popov, D. S. Sil’vestrov, O. I. Klesov, I. K. Matsak, M. P. Moklyachuk, O. O. Kurchenko, N. M. Zinchenko and A. B. Kachyns’kyj.

M. I. Yadrenko is well known as a remarkable teacher. His lectures are characterized by mathematical rigorousness, high scientific level, and clarity of presentation. Many known experts in probability theory and mathematical statistics learned these branches of mathematics at his lectures.

M. I. Yadrenko is the author of 24 textbooks on diferent branches of mathematics, among which one should mention “Probability Theory and Mathematical Statistics” (Vyshcha Shkola, Kiev (1988)) (written together with I. I. Gikhman and A. V. Skorokhod) and an unparalleled book of problems in probability theory (written together with A. V. Skorokhod, A. Ya. Dorogovtsev, and D. S. Sil’vestrov), the English version of which was published in 1997 in the USA.

In 1995, for the first time in the Ukraine, M. I. Yadrenko began to deliver lectures on actuarial mathematics and the theory of insurance risk. Together with his disciples M. M. Leonenko, Yu. S. Mishura, and V. M. Parkhomenko, M. I. Yadrenko published the first Ukrainian textbook on econometrics and contemporary financial and actuarial mathematics. M. I. Yadrenko is one of the initiators of the introduction of the new mathematical speciality “Statistics” in the Ukraine. In 1997-2001, he headed the Statistical Aspects of Economics global international project within the framework of the TEMPUS-TACIS program of the European Community.

One should especially note the tremendous contribution of M. I. Yadrenko to the training of talented young mathematicians. For more than 40 years, he has been an organizer of mathematical circles for scholars and school mathematical competitions at diferent levels. Since 1970, M. I. Yadrenko has headed the jury of All Ukrainian mathematical competitions for scholars and students. For many years, he has delivered TV lectures on mathematics for scholars. M. I. Yadrenko founded “U Sviti Matematyky”, an unparalleled journal for scholars, and was its editor since 1970. He also headed All Ukrainian correspondence competitions in physics and mathematics organized by “U Sviti Matematyky”. The facts presented above do not exhaust the versatile activities of M. I. Yadrenko. He was the Vice-President of the Ukrainian Mathematical Society, a member of the bureau of the Department of Mathematics at the Ukrainian National Academy of Sciences, the Editor in Chief of the “Prykladna Statystyka, Aktuarna ta Finansova Matematyka” scientific journal, a deputy editor of the “Theory of Probability and Mathematical Statistics” journal, and a member of the Editorial Board of the “Random Operators and Stochastic Equations” international journal. For his scientific and pedagogical activities, M. I. Yadrenko was awarded numerous medals. In particular, he was awarded State Prize of Ukraine (2004).