Viscosity solutions of general viscous Hamilton-Jacobi equations

We present comparison principles, Lipschitz estimates and study state constraints problems for degenerate, second-order Hamilton-Jacobi equations.Comment: 35 pages, minor revisio

Quantitative homogenization in a balanced random environment

We consider discrete non-divergence form difference operators in an i.i.d. random environment and the corresponding process--the random walk in a balanced random environment in $\mathbb{Z}^d$. We first quantify the ergodicity of the environment viewed from the point of view of the particle. As a consequence, we quantify the quenched central limit theorem of the random walk with an algebraic rate. Furthermore, we prove algebraic rate of convergence for homogenization of the Dirichlet problems for both elliptic and parabolic non-divergence form difference operators.Comment: 36 pages, 1 figur