Professor Pao-Liu Chow            Department of Mathematics       Wayne State University, Michigan, USA

Abstract: The filtering theory is an important subject in information and system sciences. The talk will begin with a brief review of the early development of linear filtering theories due to N. Wiener and then by R.E. Kalman in 1960’s. To extend the Kalman’s filtering theory to a nonlinear system, several researchers had attempted to develop a nonlinear filtering theory which could be implemented online. So far the most promising theory was due to M. Zakai. He showed that an un-normalized, conditional probability density function solves a Cauchy problem for a stochastic parabolic equation, known as Zakai equation. In this talk we shall consider approximate solutions to this equation by a discrete-time Galerkin scheme. It will be shown that, under suitable assumptions, the approximate solutions converge almost surely at certain known rates depending on the dimension of the filter and the approximation parameters. Remarks will be made about challenging computational problems about this equation and some other random differential equations.

About the Speaker: Pao-Liu Chow (周宝鎏) obtained his Ph.D. degree in the Rensselaer Polytechnic Institute (RPI), Troy, New York in 1967 and then came to Department of Mathematics and Courant Institute of Mathematical Sciences, New York University as Assistant Professor. In 1972, he moved toWayne State University in Michigan and became Associate Professor for the Department of Mathematics, moving up to Full Professor in 1977. He was appointed as Chairman of Department of Mathematics, Wayne State University from 1990 to 1995. Professor Pao-Liu Chowis known for his work in Stochastic Partial Differential Equations, Stochastic Control and Estimation, Applied Mathematics. He serves on editorial boards for a number of leading international research journals and is the author of two books and over 100 peer-reviewed journal papers.

Date&Time: October 12, 2012 (Friday), 10:30 - 11:30 a.m.
Location: 606 Conference Room, No.3 Heqing Road, Haidian District