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

Abstract: We consider a weakly interacting Markovian mean-field particle system in a fast varying environment. The particles evolve in the slow time scale and the environment process evolves in the fast time scale. The system is ``fully coupled”, i.e., the evolution of the particles depend on the state of the environment, and the environment itself changes its state depending on the empirical measure of the system of particles. For this two time scale mean-field model, we prove a process-level 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.

This talk is based on joint work with Rajesh Sundaresan.

probability

Audience: advanced learners

Bangalore Probability Seminar

Series comments: The link to zoom meeting can be found on the seminar's google calendar - www.isibang.ac.in/~d.yogesh/BPS.html