Transportation cost inequalities for stochastic reaction-diffusion equations with L\'evy noises and non-Lipschitz reaction terms

TL;DR

This paper establishes transportation cost inequalities for the invariant measures and path laws of stochastic reaction-diffusion equations driven by Lévy noises with non-Lipschitz reactions, using Galerkin approximations.

Contribution

It proves $W_1H$ transportation inequalities for these equations' invariant measures and process laws, extending the understanding of their probabilistic properties.

Findings

Transportation inequalities hold for invariant measures.

Transportation inequalities hold for process-level laws.

Results apply to equations with non-Lipschitz reactions and Lévy noise.

Abstract

For stochastic reaction-diffusion equations with L\'evy noises and non-Lipschitz reaction terms, we prove that $W_1H$ transportation cost inequalities hold for their invariant probability measures and for their process-level laws on the path space with respect to the $L^1$-metric. The proofs are based on the Galerkin approximations.