RG 2402/1: Rough Path Theory and Random Dynamic Systems (SP 04)

Rough paths theory and its extensions allow to analyse the solution to stochastic (partial) differential equations (S(P)DE) which could not be solved up to now. We will study the long time behaviour of these solutions. The theory of random dynamical systems (RDS) is the perfect tool for doing this. We consider the question of existence, uniqueness and convergence towards invariant measures, stability, existence of attractors, invariant manifolds and random cohomologies for solutions to rough differential equations and globally well-posed stochastic SPDE.