Strong existence and uniqueness of solutions of SDEs with time dependent Kato class coefficients

：张土生（中国科技大学）
：2021-11-22 15:00
：腾讯会议ID 777687790（无密码）

报告人：张土生（中国科技大学）

时  间：11月22日下午15:00

地  点：腾讯会议ID 777687790（无密码）

内容摘要:

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. 

个人简介：

 张土生教授是国际知名的概率论专家，中国科技大学和英国曼切斯特大学教授，曾入选长江学者。主要从事随机（偏）微分方程, 大偏差, 狄氏型等方面研究。张土生教授在《Annals of Probability》,《Probability Theory and Related Fields》等国际权威杂志上发表论文160余篇,出版专著2部。现担任《Stochastic Processes and Applications 》, 《Journal of Theoretical Probability》, 《Communications in Mathmatics and Statistics 》等国际著名刊物的编委。

 

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