Systems of Reflected Stochastic PDEs in a Convex Domain: Analytical Approach

TL;DR

This paper proves the existence and uniqueness of solutions for systems of reflected quasilinear stochastic PDEs in convex domains using an analytical approximation method.

Contribution

It introduces a novel analytical approach for solving reflected stochastic PDE systems in convex domains, advancing the theoretical understanding of such equations.

Findings

Established existence and uniqueness of solutions.

Developed an approximation method for reflected SPDEs.

Extended analytical techniques to convex domains.

Abstract

In this paper, we establish an existence and uniqueness result for system of quasilinear stochastic partial differential equations (SPDEs for short) with reflection in a convex domain in R^k by analytical approach. The method is based on the approximation of the penalized systems of SPDEs.