报告时间：2022/10/11 9:00-11:00

腾讯会议：478-638-378

报告题目：Irreducibility of SPDEs driven by pure jump noise

摘要：The irreducibility is fundamental for the study of ergodicity of stochastic dynamical systems. In the literature, there are very few results on the irreducibility of stochastic partial differential

 equations (SPDEs) and stochastic differential equations (SDEs) driven by pure jump noise. The existing methods on this topic are basically along the same lines as that for the Gaussian case. They heavily rely on the fact that the driving noises are additive type and more or less in the class of stable processes. The use of such methods to deal with the case of other types of additive pure jump noises appears to be unclear, let alone the case of multiplicative noises.

In this paper, we develop a new, effective method to obtain the irreducibility of SPDEs and SDEs driven by multiplicative pure jump noise. The conditions placed on the coefficients and the driving noise are very mild, and in some sense they are necessary and sufficient. This leads to not only significantly improving all of the results in the literature, but also to new irreducibility results of a much larger class of equations driven by pure jump noise with much weaker requirements than those treatable by the known methods. As a result, we are able to apply the main results to SPDEs with locally monoton coefficients, SPDEs/SDEs with singular coefficients, nonlinear Schrodinger equations, Euler equations etc. We emphasize that under our setting the driving noises could be compound Poisson processes, even allowed to be infinite dimensional. It is somehow surprising.

报告人简介： 翟建梁，于2010年获中国科学院数学与系统科学研究院理学博士，现为中国科学技术大学副教授。主要研究方向是Levy过程驱动的随机偏微分方程。已发表和接受论文30余篇, 包括“JEMS”、“J. Funct. Anal.”、“J. Math. Pures Appl.”等国际重要杂志。主要学术贡献：Levy过程驱动的随机偏微分方程的鞅解存在性和马氏选择、强解存在唯一性、时间正则性、大偏差原理、中偏差原理，不可约性等；平稳测度支撑的渐近行为的研究。