Existence and uniqueness of invariant measures for SPDEs with two reflecting walls

TL;DR

This paper investigates stochastic partial differential equations with two reflecting walls driven by space-time white noise, establishing the existence and uniqueness of invariant measures and demonstrating the strong Feller property under certain conditions.

Contribution

It provides new results on the existence, uniqueness, and regularity properties of invariant measures for SPDEs with reflecting boundaries driven by space-time white noise.

Findings

Existence of invariant measures established

Uniqueness of invariant measures proven

Strong Feller property demonstrated

Abstract

In this article, we study stochastic partial differential equations with two reflecting walls, driven by space-time white noise with non-constant diffusion coefficients under periodic boundary conditions. The existence and uniqueness of invariant measures is established under appropriate conditions. The strong Feller property is also obtained.