Flux large deviations of weakly interacting jump processes via well-posedness of an associated Hamilton-Jacobi equation
Richard KRAAIJ (TU Delft - Applied Probability)
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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.