Distinguished Lecture——Irreducibility and ergodicity of SPDEs driven by pure jump noise
报告人：张土生 (中国科学技术大学)
时间：2025-05-16 14:00-15:00
地点：智华楼四元厅
报告摘要：In this paper, we develop a new and 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. As an application of our main results, we remove all the restrictive conditions on the driving noises in the literature, and derive new irreducibility results of a large class of equations driven by pure jump noise, including SPDEs with locally monotone coefficients, SPDEs/SDEs with singular coefficients, nonlinear Schrödinger equations etc. We emphasize that under our setting the driving noises could be compound Poisson processes, even allowed to be infinite dimensional. As further applications of the main results, we obtain the ergodicity of multi-valued, singular stochastic evolution inclusions such as stochastic 1-Laplacian evolution(total variation flow), stochastic sign fast diffusion equation, stochastic minimal surface flow, stochastic curve shortening flow, etc.
报告人简介：张土生，中国科学技术大学教授，国际知名概率论专家，曾任英国曼彻斯特大学终身教授和概率统计系主任， 入选国家级高层次人才计划。现担任Stochastic Processes and Their Applications、Journal of Theoretical Probability、Applied Mathematics and Optimization等国际著名刊物的编委。主要研究成果包括两部由Springer出版的专著，以及一百余篇发表在国际一流学术期刊的论文。他的突出贡献主要集中在以下领域：1. 随机微分方程；2. 随机偏微分方程；3. 马氏唯一性；4. Dirichlet 型；5. 大偏差的研究。
