Well-posedness and homogenization of stochastic Hamilton-Jacobi equations
Benjamin Seeger · arXiv (Cornell University) · 2016
In this paper we consider a class of stochastic Hamilton-Jacobi equations with spatial dependence. We prove that these equations admit unique solutions, and we show that the solution operator is continuous with respect to the path. We then consider the same equations with oscillatory spatial dependence, and prove that the solutions converge locally uniformly to the solution of a stochastic Hamilton-Jacobi equation with a spatially homogenous Hamiltonian. This homogenization result is stronger than one appearing in a previous work by the author, in which the arbitrary continuous path is replaced by a family of smooth approximations to the path.