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.

arXiv comment45 pages, 12 figures

References in corpus (3)

• Averaging of Hamiltonian flows with an ergodic component
• On perturbations of generalized Landau-Lifshitz dynamics
• Diffusion in the presence of cells with semi-permeable membranes