Irreducibility of SPDEs driven by pure jump noise

一、报告题目 Irreducibility of SPDEs driven by pure jump noise 二、主讲人 崔建梁（中国科学技术大学） 三、报告时间 2023年11月7日 19:00-20:00 四、报告地点 Zoom：742-475-3864 五、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. 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. 六、主讲人简介 Jianliang Zhai received his PhD from Academy of mathematics and system science, Chinese Academy of Sciences in 2010. Currently, he is an associate Professor in the School of Mathematical Sciences at The University of Science and Technology of China. His research interests are in probability theory, especially in stochastic partial differential equations driven by Levy noise. 七、主办单位 非线性期望前沿科学中心 数学与交叉科学研究中心 中俄数学中心青岛基地