题目：Random Periodicity: Theory and Modelling

报告人：赵怀忠 教授

（英国Loughborough大学数学系教授，山东大学）

Abstract：

Random periodicity is ubiquitous in the real world. In this talk, I will provide the concepts of random periodic paths and periodic measures to mathematically describe random periodicity. It is proved that these two different notions are ''equivalent''. Existence and uniqueness of random periodic paths and periodic measures for certain stochastic differential equations are proved. An ergodic theory is established. It is proved that for a Markovian random dynamical system, in the random periodic case, the infinitesimal generator of its Markovian semigroup has infinite number of equally placed simple eigenvalues including $0$ on the imaginary axis. This is in contrast to the mixing stationary case in which the Koopman-von Neumann Theorem says there is only one eigenvalue $0$, which is simple, on the imaginary axis. Geometric ergodicity for some stochastic systems is obtained. The sufficient condition for the existence of the density of Periodic Measure is given and Fokker-Planck equation is obtained.Possible applications e.g. in stochastic resonance will be discussed.

时间：2019年12月23日（周一）下午15:30 - 16:30

地点：565net必赢客户端本部教二楼527教室

联系人：刘兆理

欢迎全体师生积极参加！