Averaging in the case of multiple invariant measures for the fast system

Mark Freidlin; Leonid Koralov

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arXiv · 2002.10019

Averaging in the case of multiple invariant measures for the fast system

Mark Freidlin·Leonid Koralov

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Abstract

We consider the averaging principle for deterministic or stochastic systems with a fast stochastic component (family of continuous-time Markov chains depending on the state of the system as a parameter). We show that, due to bifurcations in the simplex of invariant probability measures of the chains, the limiting system should be considered on a graph or on an open book with certain gluing conditions in the vertices of the graph (or on the bifurcation surface).

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Mark Freidlin, Leonid Koralov. 2020-02-24. Averaging in the case of multiple invariant measures for the fast system. https://arxiv.org/abs/2002.10019

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