LARGE DEVIATIONS OF MEAN-FIELD INTERACTING PARTICLE SYSTEMS IN A FAST VARYING ENVIRONMENT

• 成果类型: Article
• 署名作者: Yasodharan, Sarath; Sundaresan, Rajesh
• 署名单位: Indian Institute of Science (IISC) - Bangalore
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/21-AAP1718
• 发表日期: 2022
• 页码: 1666-1704
• 关键词: large-time; diffusion; LIMITS; sdes

摘要

This paper studies large deviations of a fully coupled finite state meanfield 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.