Algebraic Error Estimates for the Stochastic Homogenization of Uniformly Parabolic Equations

TL;DR

This paper develops an algebraic error estimate for stochastic homogenization of fully nonlinear uniformly parabolic equations in random media, extending methods from elliptic equations to parabolic cases.

Contribution

It introduces a novel algebraic error estimate for stochastic homogenization of parabolic equations, adapting techniques from elliptic homogenization.

Findings

Established an algebraic error bound for stochastic homogenization

Extended elliptic homogenization methods to parabolic equations

Provided a quantitative framework for error analysis in random media

Abstract

This article establishes an algebraic error estimate for the stochastic homogenization of fully nonlinear uniformly parabolic equations in stationary ergodic spatio-temporal media. The approach is similar to that of Armstrong and Smart in the study of quantitative stochastic homogenization of uniformly elliptic equations.