报告题目：SDE driven by multiplicative cylindrical $\alpha$-stable noise with distributional drift

报告人：吴明燕  厦门大学

报告时间：12月1日 10：00-11：00

报告地点：新楼308

摘要：

In this talk, we will introduce the following stochastic differential equation driven by a non-degenerate symmetric $\alpha$-stable process in $\mathbb{R}^d$ with $\alpha \in (1,2)$:\begin{align*}{\mathord{{\rm d}}} X_t=b(t,X_t){\mathord{{\rm d}}} t+\sigma(t,X_{t-}){\mathord{{\rm d}}}L_t^{(\alpha)},\ \ X_0 =x \in \mathbb{R}^d,\end{align*}where $b$ belongs to $L^\infty(\mathbb{R}_+;\mathbf{C}^{-\beta}(\mathbb{R}^d))$ with some $\beta\in(0,\alpha-1)$, and $\mathbf{C}^\beta$ denotes a Besov space (see Definition \ref{iBesov} below). The coefficient $\sigma:\mathbb{R}_+\times \mathbb{R}^d \to \mathbb{R}^d \otimes \mathbb{R}^d$ is a measurable matrix-valued function. The noise $L_t^{(\alpha)}=(L_t^{(\alpha),1},...,L_t^{(\alpha),d})$ consists of independent $1$-dimensional symmetric $\alpha$-stable processes, and is referred to as a cylindrical $\alpha$-stable process. We will present the well-posedness result of weak solutions to the SDE, and provide quantitative stability estimates with respect to the drift coefficients.This is a joint work with Zimo Hao.