报告题目： Limit theorems for random processes with immigration at the epochs of a renewal process

报告人：Alexander Iksanov，教授，乌克兰基辅大学
照片：

邀请人：董从造  
报告时间：2018年12月25日（周二）下午2:00-2:40
报告地点：信远楼II206数统院报告厅
报告人简介：Dr. Alexander Iksanov is now professor of Taras Shevchenko National University of Kyiv (KNU), and since 2014, is the Head of Operations Research Department of KNU. Professor Iksanov has been teaching at the Faculty of Computer Science and Cybernetics of KNU ever since 1996 and was awarded the degree of full professor in 2011. Earning the degree of a specialist in applied mathematics from KNU in 1995, professor Iksanov defended his PhD (statistics of shot noise processes) and habilitation (fixed points of the smoothing transforms) theses in 2000.
Professor Iksanov is the Associate Editor of the journal "Theory of Stochastic Processes" and the member of two research councils in Kyiv for PhD and habilitation defenses. Since 2001, Dr. Iksanov has been a recipient of numerous fellowships granted by Austria, France, Germany, Great Britain, Lithuania, the Netherlands, Poland, and so on. In June of 2017 he delivered a 48-hour graduate course at Xidian University titled Elements of Renewal Theory with Applications.
According to Mathscinet, professor Iksanov is the author of 78 publications. In terms of Google Scholar his h-index is 19, the number of citations is 1152. He has published 2 monographs, written over 10 lecture notes, and authored more than 70 research articles in various international probability journals such as Annals of Probability, Annals of Applied Probability, Bernoulli, Stochastic Processes and Their Applications, Electronic Communications in Probability, Electronic Journal of Probability, etc.
In 2018 the research scope of professor Iksanov includes:
(1)Random Discrete Structures (Random Compositions, Coalescents, Branching Random Walk with Complex Parameter etc.);
(2)Functional Limit Theorems;
(3)Random Processes with Immigration;
(4)Random Walk in a Sparse Random Environment; and
(5)Applications of the Renewal Theory.

报告摘要：I shall talk about random processes with immigration at the epochs of a renewal process. This class of random processes which alternatively may be called renewal shot-noise(散粒噪声/散弹噪声：通信设备中的有源器件(如电真空管）中，由于电子发射不均匀性所引起的噪声；由Schottky于1918年研究此类噪声时，用子弹射入靶子时所产生的噪声得名) processes with random response functions includes perpetuities, branching processes with immigration, the number of busy servers in the GI/G/infinity queue and many others. I shall discuss one limit theorem in which the processes, properly rescaled, converge weakly in the Skorokhod space endowed with the J1-topology without normalization and centering. The limit processes are stationary processes with immigration.