The exponential resolvent of a markov process and large deviations for markov processes via hamilton-jacobi equations

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Abstract

We study the Hamilton-Jacobi equation f − λHf = h, where Hf = e−f Aef 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 equa-tion, 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).

Original languageEnglish
Article number134
Pages (from-to)1-39
Number of pages39
JournalElectronic Journal of Probability
Volume25
DOIs
Publication statusPublished - 2020

Keywords

  • Hamilton-Jacobi equations
  • Large deviations
  • Markov processes
  • Non-linear resolvent

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