2014-12-94

Obituarytheory after coming back to Kiev in 1957. The results of thoseinvestigations obtained by him over 1957–1961 formed thebasis of his doctoral dissertation and his first book “Studies inthe theory of random processes”, published by Kiev Universityin 1961. The assertions expounded in that book, as wellas the methods used by A. V. Skorokhod for proving them,were fundamentally different from those that were typical inthe theory of stochastic differential equations at that time: thebook was full of new ideas, new methods and new results.At the beginning of the 1960s, A. V. Skorokhod publishedseveral articles devoted to the theory of stochastic differentialequations that described diffusion processes in a region with aboundary. Those were pioneering works and they stimulated areal stream of investigations on the topic at many probabilisticcentres around the world. It should be said that the theoryof stochastic differential equations has now become one ofthe most essential acquisitions of the whole of mathematicsin the second half of the 20th century and it is impossible toover-estimate the contribution of A. V. Skorokhod.The full list of Skorokhod’s publications consists of morethan 300 articles published in various journals, and 23 monographs,some of them written jointly with co-authors (thenumber of monographs should be increased to 45 if translationsare taken into account). Under Skorokhod’s supervision,more than 50 graduate students defended their candidate dissertationsand 17 of his disciples became doctors of mathematics.It should be added that A. V. Skorokhod paid considerableattention to popularising mathematics amongst schoolchildren.He was Rector of the University of Young Mathematicianswhich was active for 10 years at the Institute ofMathematics in Kiev. Each academic year at that universitystarted with a lecture delivered by A. V. Skorokhod. He published16 textbooks and popular-science books (some of themwith co-authors).A. V. Skorokhod was incessantly in search of new mathematicaltruth. He was able to see the gist of a problem, to findout an original unexpected approach to it and to create an adequatemethod for solving it. Besides, he was in the habit ofthinking over problems thoroughly every day. Owing to hisintense work day after day, the creative spark given to himfrom God became a bright shining star of the first magnitudeon the mathematical frontier.A brief biographical outlineAnatoli Vladimirovich Skorokhod was born 10 September1930 in the town of Nikopol, Dnipropetrovsk region (previouslyEkaterinoslavskaya province) to a family of teachers.Anatoli spent his childhood in Southern Ukraine. His parentstaught in rural schools around Nikopol. Anatoli’s childhoodtook place during the very difficult 1930s: the ruin after theRevolution and the Civil War of 1919–1922, collectivisationof peasants, dispossession, exile and hunger.Anatoli’s father Vladimir Alexseevich taught mathematics,physics and astronomy, primarily in high school. A greatteacher, he was erudite and had a sharp analytical mind. Fromhim, Anatoli inherited an inquisitive, analytical mind and acritical attitude toward everything. His father played a majorrole in the choice of his eldest son’s profession. Anatoli’smother Nadezhda Andreevna taught Russian and Ukrainianliterature, history, music and singing, as well as mathematics.Nadezhda Andreevna had many different talents. She wasa good musician and had a vivid dramatic talent. NadezhdaAndreevna also had good writing skills. Boasting an excellentstyle, she wrote scripts, stories and poems.Anatoli entered elementary school at the age of seven. Hisstudies were interrupted by World War II. The part of Ukrainewhere the Skorokhods were living was occupied at the beginningof the war.The post-war years in Southern Ukraine were years ofpoor harvest and, in 1946, trying to escape from the hunger,the family moved to live in Kovel, a town at Volyn in the westernregion of Ukraine. Their father was offered a position ofschool principal. Studying in high school was easy for Anatoliwithout any apparent effort. He was excellent in all subjects.Despite always being interested in mathematics, duringhis school years Anatoli did not feel any predestination to becomea mathematician.After his graduation with a gold medal from high schoolin 1948, Anatoli followed the advice of his father and submittedhis documents to the Kiev State University (named afterTaras Shevchenko) and was enrolled in the Faculty of Mechanicsand Mathematics.Skorokhod’s scientific work began in his student years.Under the supervision of Boris Vladimirovich Gnedenko (atthat time Chairman of the Department of Probability Theory)and Iosif Illich Gikhman (then an associate professor of thedepartment), Anatoli started his work in probability theory. Atthe end of his student years Skorokhod became involved in theresearch related to the famous Donsker invariance principle.During 1953–1956, Anatoli was studying in the graduateschool of Moscow State University under the supervision ofEugene Borisovich Dynkin.This period of study in this graduate school was a remarkableperiod in Skorokhod’s life in many ways. At thistime (the 1950s) in the Faculty of Mechanics and Mathematics,a broad audience of talented young people gatheredaround the great teachers of the older generation. These youngmathematicians saw their future in the service of fundamentalscience. Amongst this group, Anatoli Skorokhod was distinguishedby his independence in research work and thecourage and originality of his approaches to problem solving.According to Anatoli, the main thing that he benefitedfrom in Moscow graduate school was the seminar of his advisorE. B. Dynkin, called “Analysis, Algebra and ProbabilityTheory”.Skorokhod’s PhD thesis (his dissertation was defended inMay 1957) contained descriptions of new topologies in thespace of functions without discontinuities of the second kindand the application of them for proving limit theorems forstochastic processes. The Donsker invariance principle wasgeneralised to the case when the limit process is a generalprocess with independent increments. In the proofs of the theoremshe used the original method invented by the author,known as the “method of a single probability space”. Theimportance of the ideas of a very young mathematician wasconfirmed by the entire future development of the theory ofstochastic processes. The terms “Skorokhod topology”, “Skorokhodspace” and “Skorokhod metric” are included in all basicbooks on the theory of stochastic processes.EMS Newsletter December 2014 25