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