国产探花

荔园学者Colloquium第一百六十六期

讲座题目：Quantitative Asymptotics for Time-Inhomogeneous Levy-Driven SDEs with Asymptotically Vanishing Drifts

主讲人：王健 教授 （福建师范大学）

讲座时间：2026年5月8日15:30-17:00

讲座地点：深圳大学粤海校区汇星楼二号教室

内容摘要：In this talk, we are concerned with a class of multi-dimensional time-inhomogeneous stochastic differential equations (SDEs) driven by pure-jump Levy processes, where the drift coefficient $b(t,x)$ satisfies $\lim_{t\to \infty}b(t,x) =0$. On account of three regimes associated with  the index $\alpha$ of large jumps of the driven Levy noise, we investigate the quantitative asymptotic behavior of the corresponding rescaled processes. More precisely, for $\alpha\in (0,2)$, we prove that the rescaled processes, governed by time-inhomogeneous SDEs subject to additive processes, converge with respect to suitably chosen Wasserstein distances to time-homogeneous SDEs driven by symmetric $\alpha$-stable processes. Notably, the driving noise in the limiting SDEs depends only on large jumps of the underlying additive processes. A phase transition occurs for all values of the index $\alpha$, and a diffusive phenomenon arises whenever $\alpha\ge2$. In particular, for $\alpha>2$, we establish the ergodicity of the rescaled process by means of asymptotic pseudotrajectories.

主讲人简介：王健，福建师范大学教授。2008年博士毕业于北京师范大学，2009年获得德国洪堡基金，2014年获得日本学术振兴基金，2015年获得国家自然科学基金优秀青年基金，2022年获得国家自然科学基金杰出青年基金。

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