Tracking Properties of Trajectories On Random Attracting Sets

Abstract

The theory of random attracting sets highlights interesting properties of the asymptotic behaviour of some stochastic differential equations. In this paper some results on the relation between the dynamics on random attractors and stochastic inertial manifolds, and the dynamics in the associated random dynamical system are studied. In particular, some tracking properties of trajectories on random attractors and a general result on the asymptotic completeness of stochastic inertial manifolds are shown.