Flux large deviations of weakly interacting jump processes via well-posedness of an associated Hamilton-Jacobi equation

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Abstract

We establish uniqueness for a class of first-order Hamilton-Jacobi equations with Hamiltonians that arise from the large deviations of the empirical measure and empirical flux pair of weakly interacting Markov jump processes. As a corollary, we obtain such a large deviation principle in the context of weakly interacting processes with time-periodic rates in which the period-length converges to 0.

Original languageEnglish
Pages (from-to)1496-1528
Number of pages33
JournalBernoulli
Volume27
Issue number3
DOIs
Publication statusPublished - 2021

Keywords

  • Empirical measure and flux
  • Hamilton-jacobi equation
  • Large deviations
  • Weakly interacting jump processes

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