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

2017/11/01 by Richard C. Kraaij, Kraaij, Richard C.
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #49L25 #60F10 #60J75 #Advanced Thermodynamics and Statistical Mechanics #FOS: Mathematics #Mathematical Biology Tumor Growth #Probability (math.PR) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1711.00274

openalex publication_date 2017/11/01 · openalex created_date 2022/08/22 · openalex updated_date 2026/07/28

Abstract

We establish uniqueness for a class of first-order Hamilton-Jacobi equations\nwith Hamiltonians that arise from the large deviations of the empirical measure\nand empirical flux pair of weakly interacting Markov jump processes. As a\ncorollary we obtain a large deviation principle for the trajectory of the\nempirical measure and empirical flux pair of such processes. As a second\ncorollary we get same result in the setting where the jump-rates are\ntime-periodic, with period-length that decreases to 0.\n

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