2016/01/23 by Paul Dupuis, Dupuis, Paul, Kavita Ramanan +3
Economics, Econometrics and Finance · Mathematics · #60F10 #60K35 #FOS: Mathematics #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and financial applications #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.1601.06219
openalex publication_date 2016/01/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We establish a large deviation principle for the empirical measure process associated with a general class of finite-state mean field interacting particle systems with Lipschitz continuous transition rates that satisfy a certain ergodicity condition. The approach is based on a variational representation for functionals of a Poisson random measure. Under an appropriate strengthening of the ergodicity condition, we also prove a locally uniform large deviation principle. The main novelty is that more than one particle is allowed to change its state simultaneously, and so a standard approach to the proof based on a change of measure with respect to a system of independent particles is not possible. The result is shown to be applicable to a wide range of models arising from statistical physics, queueing systems and communication networks. Along the way, we establish a large deviation principle for a class of jump Markov processes on the simplex, whose rates decay to zero as they approach the boundary of the domain. This result may be of independent interest.