Speaker: Andrei Zaitsev (St.Petersburg Department of Steklov Mathematical Institute of RAS)

Date: Nov. 15 (Wednesday)

Beijing time: 15:00-16:00 (Moscow time: 10:00-11:00)

Zoom ID: 850 5203 9063 Password: 897365

Abstract：

Let $X_1,\dots, X_n,\dots$ be independent identically distributed $d$-dimensional random vectors with common distribution $F$. Then $S_n=X_1+\dots+X_n$ has distribution $F^n$ (degree is understood in the sense of convolutions). Let $$ \rho(F,G) = \sup_A |F\{A\} - G\{A\}|, $$ where the supremum is taken over all convex subsets of $\mathbb R^d$. Basic result is as follows. For any nontrivial distribution $F$ there is $c(F)$ such that $$\rho (F^n, F^{n+1})\leq \frac{c(F)}{\sqrt n} $$ for any natural $n$. The distribution $F$ is considered trivial if it is concentrated on a hyperplane that does not contain the origin. Clearly, for such $F$ $$\rho (F^n, F^{n+1}) = 1. $$

Biography:

Prof. Zaitsev is a specialist in the field of probability theory and mathematical statistics, the author of more than 100 publications, including a monograph. His main results are related to the study of sums of independent variables. In June 1978 he graduated in mathematics from the Mathematics and Mechanics Faculty of the Leningrad State University. In August 1978 was hired by the Leningrad branch of the Steklov Mathematical Institute of the USSR Academy in the laboratory of statistical methods. In December 1992, Prof. Zaitsev was elected to the position of leading scientific researcher of PDMI RAS. From March 2001 to March 2006 he worked as a scientific secretary of PDMI. Since March 2006 he is again leading researcher PDMI. From January 2005 to June 2006 and from January 2010 to the present time Prof. Zaitsev is working as a professor of the chair of probability theory and mathematical statistics at the St. Petersburg State University.