报告题目：Irreducibility Of SPDEs Driven by Pure Jump Noise

报告时间：2023-03-20  10:00-11:00

报告人：张土生 教授  中国科学技术大学

报告地点：理学院东北楼四楼报告厅

报告摘要：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 cases. They rely on 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 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, new applications apply to SPDEs with locally monotone coefficients, SPDEs/SDEs with singular coefficients, Euler equations etc.