Homogenization for¶Stochastic Hamilton-Jacobi Equations

Abstract:

Homogenization asks whether average behavior can be discerned from partial differential equations that are subject to high-frequency fluctuations when those fluctuations result from a dependence on two widely separated spatial scales. We prove homogenization for certain stochastic Hamilton-Jacobi partial differential equations; the idea is to use the subadditive ergodic theorem to establish the existence of an average in the infinite scale-separation limit. In some cases, we also establish a central limit theorem.