Large deviations for Markov jump processes with mean-field interaction via the comparison principle for an associated Hamilton-Jacobi equation

摘要

We prove the large deviation principle for the trajectory of a broad class ofmean field interacting Markov jump processes via a general analytic approachbased on viscosity solutions. Examples include generalized Ehrenfest models aswell as Curie-Weiss spin flip dynamics with singular jump rates. The main step in the proof of the large deviation principle, which is ofindependent interest, is the proof of the comparison principle for anassociated collection of Hamilton-Jacobi equations. Additionally, we show that the large deviation principle provides a generalmethod to identify a Lyapunov function for the associated McKean-Vlasovequation.