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2020 The exponential resolvent of a Markov process and large deviations for Markov processes via Hamilton-Jacobi equations
Richard C. Kraaij
Electron. J. Probab. 25: 1-39 (2020). DOI: 10.1214/20-EJP539

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 an 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 (2006).

Citation

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Richard C. Kraaij. "The exponential resolvent of a Markov process and large deviations for Markov processes via Hamilton-Jacobi equations." Electron. J. Probab. 25 1 - 39, 2020. https://doi.org/10.1214/20-EJP539

Information

Received: 8 January 2020; Accepted: 22 October 2020; Published: 2020
First available in Project Euclid: 29 October 2020

MathSciNet: MR4169175
Digital Object Identifier: 10.1214/20-EJP539

Subjects:
Primary: 47H20, 60F10
Secondary: 49L25, 60J25, 60J35

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