报告人：张土生教授

主持人：加拿大纽芬兰纪念大学Xiaoqiang Zhao教授

报告题目：Strong existence and uniqueness of solutions of SDEs with time dependent Kato class coefficients

摘要：Consider stochastic differential equations (SDEs) in $\Rd$: $dX_t=dW_t+b(t,X_t)\d t$, where $W$ is a Brownian motion, $b(\cdot, \cdot)$ is a measurable vector field. It is known that if $|b|^2(\cdot, \cdot)=|b|^2(\cdot)$ 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 $\K_{d,\a}$ for some $\a \in (0,2)$ ($\a$ 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.

报告时间：2022年1月12日9:30-11:30

报告地点：腾讯会议   会议号：187 412 608

报告人简介：https://dsxt.ustc.edu.cn/zj_js.asp?zzid=3773