An approximation result for a class of stochastic heat equations with colored noise

TL;DR

This paper demonstrates that many stochastic heat equations with colored noise can be approximated by interacting stochastic differential equations, leading to new comparison principles and moment estimates.

Contribution

It introduces an approximation method for stochastic heat equations with colored noise using interacting SDEs, extending comparison principles and providing sharp moment estimates.

Findings

Established approximation of stochastic heat equations by interacting SDEs

Extended comparison principles for solutions

Derived sharp moment estimates

Abstract

We show that a large class of stochastic heat equations can be approximated by systems of interacting stochastic differential equations. As a consequence, we prove various comparison principles extending earlier results. Among other things, our results enable us to obtain sharp estimates on the moments of the solution. A main technical ingredient of our method is a local limit theorem which is of independent interest.