Upper Bound for Large Deviations of Reversible Diffusion Processes

TL;DR

This paper establishes an upper bound for the probability of large deviations in reversible diffusion processes, providing insights into their behavior and applications to Wasserstein diffusion.

Contribution

It introduces a new upper bound for large deviations of reversible diffusion processes, extending to the process law under certain conditions, with applications to Wasserstein diffusion.

Findings

Upper bound for finite-dimensional distributions of reversible diffusions

Extension of bounds to the entire process law under specific assumptions

Application demonstrated for Wasserstein diffusion

Abstract

For a Markov process associated with a diffusion type Dirichlet form an upper bound is shown for the law of the finite dimensional distributions of the process. Under some more assumptions on the underlaying space this is also shown for the law of the Markov process itself. In the last section we want to give an application to the Wasserstein diffusion.