Irreducibility of SPDEs driven by pure jump noise

：翟建梁（中国科技大学）
：2023-04-25 15:00
：腾讯会议ID：852-671-345（无密码）

报告人：翟建梁（中国科技大学）

时  间：2023年4月25日下午15：00

地  点：腾讯会议ID：852-671-345（无密码）

内容摘要:

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 monotone 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.

个人简介：

翟建梁，中国科学技术大学副教授，2010年获中国科学院数学与系统科学研究院博士。主要研究方向是Levy过程驱动的随机偏微分方程。已在 “J. Eur. Math. Soc.”、“J. Funct. Anal.”、“J. Math. Pures Appl.”“J. Differential Equations”、“Bernoulli”等国际重要杂志发表论文三十余篇。

 

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