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

Mark Freidlin

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arXiv · 2010.01182

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

Mark Freidlin

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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.

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Mark Freidlin. 2020-10-02. Long Time Influence of Small Perturbations and Motion on the Simplex of Invariant Probability Measures. https://arxiv.org/abs/2010.01182

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