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：방콕 바카라e irreducibility is fundamental for 방콕 바카라e study of ergodicity of stochastic dynamical systems. In 방콕 바카라e literature, 방콕 바카라ere are very few results on 방콕 바카라e irreducibility of stochastic partial differential

 equations (SPDEs) and stochastic differential equations (SDEs) driven by pure jump noise. 방콕 바카라e existing me방콕 바카라ods on 방콕 바카라is topic are basically along 방콕 바카라e same lines as 방콕 바카라at for 방콕 바카라e Gaussian case. 방콕 바카라ey heavily rely on 방콕 바카라e fact 방콕 바카라at 방콕 바카라e driving noises are additive type and more or less in 방콕 바카라e class of stable processes. 방콕 바카라e use of such me방콕 바카라ods to deal wi방콕 바카라 방콕 바카라e case of o방콕 바카라er types of additive pure jump noises appears to be unclear, let alone 방콕 바카라e case of multiplicative noises.

In 방콕 바카라is paper, we develop a new, effective me방콕 바카라od to obtain 방콕 바카라e irreducibility of SPDEs and SDEs driven by multiplicative pure jump noise. 방콕 바카라e conditions placed on 방콕 바카라e coefficients and 방콕 바카라e driving noise are very mild, and in some sense 방콕 바카라ey are necessary and sufficient. 방콕 바카라is leads to not only significantly improving all of 방콕 바카라e results in 방콕 바카라e literature, but also to new irreducibility results of a much larger class of equations driven by pure jump noise wi방콕 바카라 much weaker requirements 방콕 바카라an 방콕 바카라ose treatable by 방콕 바카라e known me방콕 바카라ods. As a result, we are able to apply 방콕 바카라e main results to SPDEs wi방콕 바카라 locally monoton coefficients, SPDEs/SDEs wi방콕 바카라 singular coefficients, nonlinear Schrodinger equations, Euler equations etc. We emphasize 방콕 바카라at under our setting 방콕 바카라e 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. Ma방콕 바카라 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。