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

Journal article (2021)

Authors

R.C. Kraaij Applied Probability - EEMCS
Research Group
Applied Probability (EEMCS) (TU Delft)
Copyright: © 2021 R.C. Kraaij
DOI
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https://doi.org/10.3150/20-BEJ1281
Large deviations Hamilton-jacobi equation Empirical measure and flux Weakly interacting jump processes
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Published Date

2021

Language

English

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Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Delft Institute of Applied Mathematics

Research Group

Applied Probability

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.