Models of Random Walks with
Different Limit Behaviour
报告专家：Prof. Jordan Stoyanov（Bulgarian Academy of Sciences &Shandong University）
报告时间：7月1日（星期二）下午3:00-4:00
报告地点：数学学院西202
报告摘要：We start with the classical Frechet-Shohat theorem, called also `second limit theorem’, having its origins in works by Chebyshev and Markov, 19th c. This theorem ensures a weak convergence of distributions in terms of the moments/cumulants. Then we consider a few models of a random walk, say S_n = X_1 + … + X_n, n = 0, 1, …, based on a sequence of random variables {X_j}. Our goal is to analyse the limit behaviour, as n goes to infinity, of S_n or of the quantity (S_n)^* = (S_n – E[S_n])/(stand. dev.). As expected, in many cases the CLT holds. However, a few models of random motions will be described when the limit of S_n, or of (S_n)^*, is a bounded interval, which may look surprising. Among the explicit limiting distributions are arcsine, beta or infinite convolution of uniforms.
专家简介：JS is Honorary Professor of Bulgarian Academy of Sciences and Visiting Prof. at Shandong University. Graduated from Moscow State University earning his scientific degrees in Probability Theory under the supervision of Academician Albert Shiryaev of the Kolmogorov’s School in Probability. JS worded in Bulgaria, and was visiting professor at many universities all over the world. JS has published more than 80 papers and 5 books. Well-known is his book “Counterexamples in Probability”, three editions in English and two in Russian.
邀请人：胡泽春
