Abstract
We consider the averaging principle for deterministic and 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 the nontrivial structure of the simplex of invariant probability measures of the chains, the limiting system should be considered on a graph with certain gluing conditions at the vertices of the graph.
Acknowledgments
While working on this article, L. Koralov was supported by the ARO grant W911NF1710419, the University of Maryland Research and Scholarship Award, and the Simons Fellowship (award number 678928).
Citation
M. Freidlin. L. Koralov. "Averaging in the case of multiple invariant measures for the fast system." Electron. J. Probab. 26 1 - 17, 2021. https://doi.org/10.1214/21-EJP681
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