Homogenization for stochastic Hamilton-Jacobi equations

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 spatia l scales. We prove homogenization for certain stochastic Hamilton-Jacobi pa rtial differential equations: the idea is to use the subadditive ergodic th eorem to establish the existence of an average in the infinite scale-separa tion limit. In some cases, we also establish a central limit theorem.