Large Deviation in Harnack type Dirichlet spaces

TL;DR

This paper establishes a large deviation principle for reversible Markov processes within Harnack type Dirichlet spaces, linking the asymptotic behavior of these processes to the energy of their paths.

Contribution

It introduces a large deviation principle in the context of Harnack type Dirichlet spaces, connecting process asymptotics to path energy.

Findings

Large deviation principle proven for reversible Markov processes

Rate function characterized by the energy of paths

Extends understanding of process asymptotics in Dirichlet spaces

Abstract

In the framework of Harnack type Dirichlet forms, we prove a large deviation principle for the asymptotics of reversible Markov processes with rate function given by the energy of the paths.