Transportation cost inequalities for mean reflection SPDEs with white noise

TL;DR

This paper proves a quadratic transportation cost inequality for solutions to a new class of mean reflected SPDEs driven by white noise, linking solution laws with transportation costs.

Contribution

It introduces and establishes transportation inequalities for mean reflected SPDEs where reflection depends on the law of the solution, a novel approach.

Findings

Proves quadratic transportation cost inequality under the uniform norm.

Extends transportation inequalities to mean reflected SPDEs with law-dependent reflection.

Provides a new framework for analyzing solution distributions of complex SPDEs.

Abstract

We establish a quadratic transportation cost inequality under the uniform norm for solutions to mean reflected stochastic partial differential equations, a new type of equation in which the compensating reflection part depends not on the paths but on the law of the solution.