Shenzhen University School of Mathematical Sciences  

Liyuan Scholars Colloquium Session 166

Title: Quantitative Asymptotics for Time-Inhomogeneous Levy-Driven SDEs with Asymptotically Vanishing Drifts

Speaker: Professor Jian Wang (Fujian Normal University)

Time: 15:30–17:00, May 8, 2026

Location: Room 2, Huixing Building, Yuehai Campus, Shenzhen University

Abstract: 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.

Speaker Profile:  Jian Wang is a professor at Fujian Normal University. He received his Ph.D. from Beijing Normal University in 2008. In 2009, he was awarded a Humboldt Fellowship; in 2014, a Japan Society for the Promotion of Science (JSPS) Research Fellowship; in 2015, a National Natural Science Foundation of China (NSFC) Outstanding Young Scientist Grant; and in 2022, an NSFC Distinguished Young Scientist Grant.

All faculty and students are welcome!  

School of Mathematical Sciences  

May 6, 2026