Scaling Limit of Small Random Perturbation of Dynamical Systems

Fraydoun Rezakhanlou; Insuk Seo

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arXiv · 1812.02069

Scaling Limit of Small Random Perturbation of Dynamical Systems

Fraydoun Rezakhanlou·Insuk Seo

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Abstract

In this article, we prove that a small random perturbation of dynamical system with multiple stable equilibria converges to a Markov chain whose states are neighborhoods of the deepest stable equilibria, under a suitable time-rescaling, provided that the perturbed dynamics is reversible in time. Such a result has been anticipated from 1970s, when the foundation of mathematical treatment for this problem has been established by Freidlin and Wentzell. We solve this long-standing problem by reducing the entire analysis to an investigation of the solution of an associated Poisson equation, and furthermore provide a method to carry out this analysis by using well-known test functions in a novel manner.

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BibTeX RIS

Fraydoun Rezakhanlou, Insuk Seo. 2018-12-05. Scaling Limit of Small Random Perturbation of Dynamical Systems. https://arxiv.org/abs/1812.02069

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