Absolute Continuity of the Laws of the Solutions to Parabolic SPDEs with Two Reflecting Walls

TL;DR

This paper investigates the existence of probability densities for solutions to parabolic SPDEs constrained by two reflecting walls, utilizing Malliavin calculus to establish absolute continuity of their laws.

Contribution

It introduces a novel application of Malliavin calculus to prove the existence of densities for SPDEs with two reflecting barriers.

Findings

Proved the existence of densities for solutions to the SPDEs with reflecting walls.

Established conditions under which the laws of solutions are absolutely continuous.

Extended previous results to more complex boundary conditions.

Abstract

In this paper, we focus on the existence of the density for the law of the solutions to parabolic stochastic partial differential equations with two reflecting walls. The main tool is Malliavin calculus.