Large deviations of mean-field interacting particle systems in a fast varying environment

2020/08/16 by Sarath Yasodharan, Yasodharan, Sarath, Rajesh Sundaresan +1
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #60J75 #60K35 #FOS: Mathematics #Primary 60F10 #Probability (math.PR) #Secondary 60K37 #Stochastic processes and financial applications #Stochastic processes and statistical mechanics #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.2008.06855

openalex publication_date 2020/08/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper studies large deviations of a ``fully coupled" finite state mean-field interacting particle system in a fast varying environment. The empirical measure of the particles evolves in the slow time scale and the random environment evolves in the fast time scale. Our main result is the path-space large deviation principle for the joint law of the empirical measure process of the particles and the occupation measure process of the fast environment. This extends previous results known for two time scale diffusions to two time scale mean-field models with jumps. Our proof is based on the method of stochastic exponentials. We characterise the rate function by studying a certain variational problem associated with an exponential martingale.

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