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Anatolii Skorokhod memory page

Anatolii Skorokhod
at Kyiv University

Anatolii Volodymyrovych Skorokhod entered the Mechanics and Mathematics Faculty of Kyiv State University in 1948. Being a student, he started actively working on some problems of mathematical analysis and probability theory. His first research was supervised by B.V. Gnedenko and I.I. Gikhman. In his student years, Skorokhod solved several problems mostly concerning stable laws. He graduated from the University being already an author of five scientific papers. Three of them were published in leading scientific journals such as Soviet Mathematical Surveys and S.R. (Dokl.) Acad. Sci. URSS (Doklady Akademii Nauk SSSR), and two of them were published in collections of scientific papers written by students of Kyiv University. Two of Skorokhod’s early articles were translated to English and published in Selected Translations on Mathematical Statistics and Probability (1961). Skorokhod graduated from Kyiv University in 1953 and continued his research as a postgraduate student at Moscow State University under the supervision of E.B. Dynkin. Skorokhod’s work of this period already contained some revolutionary concepts and methods in the theory of stochastic processes. He introduced a new topology on the space of cadlag functions (right-continuous with left limits), which he called J-topology, or Skorokhod topology. In 1956, Skorokhod defended his Candidate Thesis “Limit theorems for random processes” and returned to Kyiv, where he began lecturing at Kyiv University. At the same time he conducted intensive scientific research. In 1961, his first monograph, “Studies in the theory of random processes (Stochastic differential equations and limit theorems for Markov processes)” was printed in the publishing house of Kyiv State University, and it was translated to English in 1965. This book was the basis for his Doctoral thesis “Stochastic differential equations and limit theorems for random processes” defended in 1962.

In 1964, Skorokhod became chair of the new Department of the Theory of Random Processes at the Institute of Mathematics of the Ukrainian Academy of Sciences, while continuing giving lectures at Kyiv University.

For his scientific achievements, Skorokhod was elected Corresponding Member of the Ukrainian Academy of Sciences in 1967.

Almost all the courses delivered by Skorokhod in Kyiv University were refined by him and published. In particular, the three-volume monograph “The theory of stochastic processes” (1971–1975) by Gikhman and Skorokhod gave a thorough systematic overview of the theory of stochastic processes. Immediately after its appearance the monograph was translated and became an extremely popular concise course on the theory of stochastic processes, aiming at an advanced reader. In 1982, Skorokhod together with Gikhman was awarded the State Prize of the Ukraine in Science and Technology for this monograph. In 1985, Skorokhod became a Full Member of the Ukrainian Academy of Sciences. In 1982 and in 2003, he was awarded the Ukrainian State Prize in Science and Technology. The Kyiv probability school was to a great extent the result of Skorokhod’s activities, and it is hard to overestimate his role in the development of this school. He had over 50 disciples, 17 of which became Doctors of Sciences. Skorokhod’s lectures at Kyiv University were both deep and accessible for students, but his contribution to the mathematical education of the youth went far beyond. He always paid considerable attention to spreading mathematical knowledge as widely as possible, giving popular mathematics lectures on television and at the University for Young Mathematicians which existed at the Institute of Mathematics in the 1970s and 1980s. Skorokhod also wrote, in collaboration with his colleagues, several elementary textbooks and popular science books. These are “Selected topics of elementary mathematics”, which had four editions, “Elements of probability theory and random processes” (three editions), and “Theory of probability. Collection of problems” (three editions including an English translation). Skorokhod is the author of 24 scientific monographs, most of which were translated, and more than 300 articles published in the scientific journals.

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