Speaker: Prof. Tusheng Zhang (张土生教授)

Time: 14:00-15:00, 7 January 2022 (Friday) (Beijing time)

Venue: T2-202

Abstract

Consider stochastic differential equations (SDEs) in R^d:dX_t=dW_t+b(t,X_t )dt, where W is a Brownian motion, b(∙, ∙) is a measurable vector field. It is known that if |b|^2 (∙,∙)=|b|^2 (∙) belongs to the Kato class K_{d,2} , then there is a weak solution to the SDE. In this article we show that if |b|^2 belongs to the Kato class K_{d,α} for some α∈(0,2) (α can be arbitrarily close to 2), then there exists a unique strong solution to the stochastic differential equations, extending the results in the existing literature as demonstrated by examples. Furthermore, we allow the drift to be time-dependent. The new regularity estimates we established for the solutions of parabolic equations with Kato class coefficients play a crucial role.

About Prof. Zhang

Professor Tusheng Zhang is an internationally recognized expert on probability. He is now a professor at University of Science and Technology of China. He was a professor at University of Manchester before joining USTC. Professor Zhang's research area is stochastic analysis. He has published two books and more than one hundred and fifty articles in leading international journals. He is also an associate editor for the following leading probability journals: <Stochastic Processes and Their Applications>，<Journal of Theoretical Probability>, < Communications in Mathematics and Statistics>.