The exponential resolvent of a Markov process and large deviations for Markov processes via Hamilton-Jacobi equations

Abstract

We study the Hamilton-Jacobi equation f - lambda Hf = h, where H f = e^{-f}Ae^f and where A is an operator that corresponds to a well-posed martingale problem. We identify an operator that gives viscosity solutions to the Hamilton-Jacobi equation, and which can therefore be interpreted as the resolvent of H. The operator is given in terms of optimization problem where the running cost is a path-space relative entropy. Finally, we use the resolvents to give a new proof of the abstract large deviation result of Feng and Kurtz.

References in corpus (2)

• A general nonconvex large deviation result II
• Strict continuity of the transition semigroup for the solution of a well-posed martingale problem

Cited by in corpus (5)

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• A large deviation principle for Markovian slow-fast systems
• Large deviations for Markov processes with switching and homogenisation via Hamilton-Jacobi-Bellman equations
• Large Deviations of Irreversible Processes