随机动力系统短期课程 — Mixing for discrete-time dynamical systems driven by a stationary process
时间：5月26日、27日、29日，10:00- 12:00
地点：智华楼四元厅
报告人：Armen Shirikyan (CY Cergy Paris University)
Abstract: The long-time asymptotics of trajectories for random dynamical systems (RDS) driven by a delta-correlated noise is understood in considerable detail. It is well known that such systems generate a Markov process and, under some non-degeneracy and regularity assumptions, possess a unique stationary distribution, which attracts the laws of all the trajectories.
The aim of this mini-course is to describe some recent results concerning the case where the driving noise is time-correlated, and hence the corresponding RDS is no longer Markovian. We shall describe a systematic procedure that allows one to reduce the system in question to a Markovian RDS in a larger phase space. Sufficient conditions ensuring the property of exponential mixing for the reduced system will be obtained, and the results will be illustrated on some evolution equations. We shall also discuss the relation of our results with the classical problem of reconstruction of random fields from their conditional laws.
The results presented in this mini-course are obtained in joint works with S. Kuksin.
简介: A. Shirikyan received his Ph.D. from Moscow State University in 1995. He worked as a junior scientist at the Institute of Mechanics (Moscow) and as a research associate at Heriot-Watt University (Edinburgh) before joining the faculty of the University of Paris-Sud in 2002. Shirikyan has been a professor at CY Cergy Paris University since 2006 and an adjunct professor at McGill University since 2017. He served as department head from 2008 to 2012, director of the master's programme from 2015 to 2019, and is currently director of the CY Institute for Advanced Studies. Shirikyan's main contributions to mathematics concern the qualitative theory of hyperbolic PDEs, the long-time behaviour of random dynamical systems, control theory for PDEs, and some aspects of non-equilibrium statistical mechanics.
