Quantitative stochastic homogenization of viscous Hamilton-Jacobi equations

TL;DR

This paper provides explicit error estimates and algebraic convergence rates for the stochastic homogenization of viscous Hamilton-Jacobi equations with random coefficients, under finite dependence assumptions.

Contribution

It offers the first explicit algebraic error bounds for the homogenization of degenerate second-order Hamilton-Jacobi equations with random coefficients.

Findings

Established explicit error estimates with high probability.

Derived algebraic convergence rates under structural conditions.

Applied to degenerate, second-order Hamilton-Jacobi equations.

Abstract

We prove explicit estimates for the error in random homogenization of degenerate, second-order Hamilton-Jacobi equations, assuming the coefficients satisfy a finite range of dependence. In particular, we obtain an algebraic rate of convergence with overwhelming probability under certain structural conditions on the Hamiltonian.