报告题目：ASYMPTOTIC ANALYSIS OF RANDOM EVOLUTIONS
     报告人：Igor Samoilenko, 副教授, 乌克兰基辅大学
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邀请人：董从造
     报告时间：2018年12月13日（周四）下午2:30-3:30
     报告地点：信远楼II206数统院报告厅
     报告人简介：Igor Samoilenko received M.Sc. degree in mathematics from Kherson State University in 1998. Since 1998 till 2001 he was a Ph.D. student in the Institute of Mathematics of the National Academy of Sciences of Ukraine in Kyiv, where he received his PhD in 2001. He was a scientist and later a senior scientist in the Department of Fractal Analysis of the Institute of Mathematics of the National Academy of Sciences of Ukraine in Kyiv till 2001-2014. He was engaged in research of functional limit theorems for different classes of random evolutions, solution of large deviation problem for processes with independent increments, models of conflict with non-annihilating opponents, etc. In 2014 he received habilitation of PhD degree from Taras Shevchenko National University of Kyiv, where he works as an associate Professor in the Department of Computer Science and Cybernetics since 2014. He took active part in international projects and has corresponding publications with scientists from University of Bonn (Germany), University of Bielefeld (Germany), Technological University of Compiegne (France). Dr. Samoilenko was awarded by the Prime of the President of Ukraine for young scientists in 2009.

     报告摘要：Transport equations are used in mathematical biology to model movement and growth of populations. Certain bacteria show the following movement pattern: periods of strait runs alternate with periods of random rotations which leads to reorientation of the cells. We may model this movement by a velocity jump process, which leads to a transport equation. Random evolutions generalize this model and describe different evolutionary or stochastic systems in random media that is defined by a switching Markov or semi-Markov process. We study such models from two points of view: limit theorems that describe their behavior on increasing time intervals and asymptotic expansions of the functionals defined for the pre-limit processes. The main tool is analysis of the generators of  corresponding complex Markov processes or renewal equations in a semi-Markov case.