报告时间：2025年10月13日（星期一）16:00-17:00

报告地点：翡翠科教楼B座1711室

报  告  人：翟建梁 副教授

工作单位：中国科学技术大学

举办单位：数学学院

报告简介：

The irreducibility is fundamental for the study of ergodicity of stochastic dynamical systems. The existing methods on the irreducibility of stochastic partial differential equations (SPDEs) and stochastic differential equations (SDEs) driven by pure jump noise are basically along the same lines as that for the Gaussian case, which are not particularly suitable for jump noise. As a result, restrictive conditions are usually placed on the driving jump noise. Basically the driving noises are additive type and more or less in the class of stable processes. 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：

翟建梁，中国科学技术大学副教授，博士生导师。2010年博士毕业于中国科学院数学与系统科学研究院，2010年进入北京大学做博士后研究工作。主要研究方向是Levy过程驱动的随机偏微分方程。主要学术贡献：纯跳Levy过程驱动的随机偏微分方程解的存在唯一性、大偏差原理、遍历性等；平稳测度支撑的渐进行为等。已在 “J. Eur. Math. Soc.”、“J. Funct. Anal.”、“J. Math. Pures Appl.”等国际重要杂志发表论文四十余篇。主持国家自然科学基金面上项目两项。