Lattice Approximations of Reflected Stochastic Partial Differential Equations Driven by Space-Time White Noise

TL;DR

This paper develops a new discretization scheme for reflected stochastic PDEs driven by space-time white noise, proving convergence through analysis of related deterministic systems and obstacle problems.

Contribution

It introduces a novel approximation method for reflected SPDEs driven by space-time white noise, with rigorous convergence analysis.

Findings

Established existence and uniqueness of solutions for Skorohod-type systems.

Proved convergence of the approximation scheme for deterministic obstacle problems.

Provided a framework for discretizing reflected stochastic PDEs with space-time white noise.

Abstract

We introduce a discretization/approximation scheme for reflected stochastic partial differential equations driven by space-time white noise through systems of reflecting stochastic differential equations. To establish the convergence of the scheme, we study the existence and uniqueness of solutions of Skorohod-type deterministic systems on time-dependent domains. We also need to establish the convergence of an approximation scheme for deterministic parabolic obstacle problems. Both are of independent interest on their own.