Long Time Influence of Small Perturbations and Motion on the Simplex of Invariant Probability Measures

Abstract

A general approach to a broad class of asymptotic problems related to long-time influence of small perturbations, of both deterministic and stochastic type, is presented in the paper. The main characteristic of this influence is a limiting motion on the simplex of invariant probability measures of the non-perturbed system in an appropriate time scale. The main tools we use in the paper are limit theorems for large deviations, modified averaging principle, and diffusion approximation.