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• W2035584443 abstract "February 27, 2007, was the 75th birthday of the eminent mathematician, Professor Vladimir Mikhailovich Zolotarev. In 1949, Vladimir entered the faculty of mechanics and mathematics of Moscow State University. As his specialization field he chose probability theory and began his studies under the supervision of Eugene Borisovich Dynkin. After graduating from the university he was recommended to graduate studies, where his advisor was Andrei Nikolaevich Kolmogorov. Other distinguished mathematicians also have had a potent effect on Zolotarev's mathematical talent. Later, he mentions more than once not only his teachers E. B. Dynkin and A. N. Kolmogorov, but also B. V. Gnedenko and Yu. V. Linnik. In his graduate studies, Vladimir begins to study the properties of stable distributions. He continues to be interested in this theme even today. At first he was dealing with the stable distributions in the scheme of summation of independent identically distributed random variables. Later, he extended the concept of a stable law to the schemes of maximum and multiplication of random variables. His studies of random variables are summarized in the monograph [1]. It has gained widespread recognition and has been translated into English. As it saw the light, the nomenclature, such as Zolotarev's theorem, Zolotarev's formula, and Zolotarev's transformation, became quite conventional. Contemporaneously with studying the properties of stable laws, Zolotarev began to work in the field of limit theorems for sums of independent random variables. His results obtained in this direction can be conventionally divided into three groups. The first group concerns refining classical theorems and convergence rate estimates. As an example, we mention the convergence rate estimate in the central limit theorem in terms of pseudomoments, which for some time remained the best estimate known. But it is even more important that the method of pseudomoments used by Zolotarev to obtain this estimate led to a new structure of convergence rate estimates in limit theorems for sums of independent random variables. His disciples have made this a powerful tool which provides us with even more sharp estimates. The principal novelty resides in that a pseudomoment allows us to recognize the contribution of every individual summand to the whole estimate. The notions of a center and a scatter (spread) introduced by Zolotarev turn out to be indispensable in establishing the weak compactness of sequences of sums of independent random variables which have no finite moments and allowed us to extend limit theorems, previously known to be valid, under quite strict moment conditions to such variables. Zolotarev's second group of results gathers together the results whose essence reduces to weakening the condition of independence of random variables so that the limit theorems remain true. The third group concerns the so-called nonclassical scheme of summation. The cornerstone of this scheme consists of breaking the habitual pattern, where an individual summand does not influence the form of the limit distribution. In the nonclassical summation theory an individual summand is allowed to play a discernible part. It is fair to say that Vladimir Zolotarev is one of the fathers of this direction in the theory of summation of random variables. He has generalized the results of his predecessors, P. Lévy and Yu. V. Linnik, who on the heuristic level of reasoning pointed to the possibility of a new approach to limit theorems for sums of independent random variables, and developed a self-sufficient theory of summation of random variables, now referred to as nonclassical. The theory of probability metrics built by Zolotarev underlies the novel viewpoint of limit theorems of probability theory as stability theorems. Zolotarev summarizes his studies in this field in the monograph [3], which immediately became a widely used source for new investigations. In 1997, a revised and enlarged version of this monograph was published in English [4]. Along with sums of random variables, Vladimir Zolotarev deals with more general asymptotic schemes. In particular, together with his Hungarian colleague L. Szeidl, Zolotarev has made an essential contribution to the asymptotic theory of random polynomials. Their joint results are presented in the monograph [6]. Investigating the asymptotic properties of sums of independent random variables, Vladimir Zolotarev came to related studies in the theory of stochastic processes and queueing theory. He and his colleagues analyze the stability and continuity of queueing systems with the use of related concepts of the theory of summation of random variables. The quantitative characteristics of these properties suggested by Zolotarev led to a deeper understanding of these phenomena. Speaking of the results obtained by Vladimir Zolotarev, we must say that he masterfully manages to use both modern and classical technique of analysis. Zolotarev enriches the store of probability theory by a series of new analytic methods and tools; it suffices to mention the thorough study of theorems of classical analysis, harmonic analysis, and the theory of special functions. Zolotarev also clears up how to use the Mellin–Stieltjes transforms in probability theory. Modern probability theory plays an important role in many natural sciences. For example, modern statistical physics becomes infeasible without using the fundamental concepts of probability theory. Vladimir Zolotarev has given many talks on how to apply probability theory to explaining various phenomena in physics, genetics, and geology. Together with V. V. Uchaikin he wrote the monograph [5], where one finds plenty of applications of stable laws explaining a series of physical and economical phenomena. In 1956, A. N. Kolmogorov founded the journal Theory of Probability and Its Applications. From the very beginning, Vladimir Zolotarev took an active part in the operation of the journal. From the day of foundation to 1966 he was the executive secretary; from 1967 to 1990 the deputy editor-in-chief; and from 1991 to the present he is a member of the advisory board. Vladimir Zolotarev founded the series of issues Stability Problems for Stochastic Models of the Journal of Mathematical Sciences, being its editor-in-chief. He also heads the editorial board of the series of monographs Modern Probability and Statistics published by VSP/Brill (The Netherlands). Vladimir Zolotarev is the initiator and continuous leader of the international scientific seminar on stability problems of stochastic models, widely known as the Zolotarev seminar. From 1973, twenty-six sessions of this seminar have been held in various countries. These sessions take place almost every year and attract about a hundred participants from diverse countries. Vladimir Zolotarev does much to popularize science. In the brochure [2] he presented an exciting story about stable laws and their applications. At the same time he created two educational films about fundamental limit theorems of probability theory. A crowd of youthful science enthusiasts is always gathering around him. Many of his pupils have become reputable specialists in various fields of mathematics. The scientific school of Vladimir Zolotarev is highly regarded. Friends and colleagues of Zolotarev love and appreciate him because he is a man of principle, well-wishing and tenderhearted, ready to stand by and assist. Devoting heart and soul to science, he demands the same from his colleagues and students. The scientific society highly appreciates the contributions of Vladimir Zolotarev. In 1971, for a series of works on limit theorems for sums of independent random variables, the Presidium of the Academy of Sciences of the USSR awarded him the Markov prize. We wish Vladimir Zolotarev many years of good health and continued activity." @default.
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• W2035584443 title "On the 75th Birthday of V. M. Zolotarev" @default.
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