The stochastic reflection problem with multiplicative noise

TL;DR

This paper investigates the existence and uniqueness of solutions to a stochastic reflection problem involving linear parabolic equations with multiplicative Gaussian noise, advancing understanding of stochastic partial differential equations with boundary constraints.

Contribution

It introduces new results on the well-posedness of stochastic reflection problems with multiplicative noise, a topic not extensively covered before.

Findings

Proved existence of solutions under certain conditions.

Established uniqueness of solutions.

Analyzed the impact of multiplicative Gaussian noise on boundary reflection.

Abstract

This work is concerned with existence and uniqueness of solutions to the reflection problem for linear parabolic equation with multiplicative Gaussian noise.