Abstract:
We consider a discrete-time random dynamical system (RDS) in a separable Hilbert space. It is assumed that the random inputs driving the system belong to a compact metric space and form a stationary sequence. We first describe a systematic procedure allowing one to reduce the problem in question to a Markovian RDS in a larger phase space. We next study the large-time asymptotics of trajectories of the reduced system and show how they can be used to draw conclusion about the original problem. Various applications will also be discussed. The results presented in this talk are obtained in joint works with S. Kuksin.
Biography:
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.
Seminar by the NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai
This event is open to the NYU Shanghai community and Math community.