  We prove, under some assumptions, the existence of correctors for the
stochastic homoge-nization of of " viscous " possibly degenerate
Hamilton-Jacobi equations in stationary ergodic media. The general claim is
that, assuming knowledge of homogenization in probability, correctors exist for
all extreme points of the convex hull of the sublevel sets of the effective
Hamiltonian. Even when homogenization is not a priori known, the arguments
imply existence of correctors and, hence, homogenization in some new settings.
These include positively homogeneous Hamiltonians and, hence, geometric-type
equations including motion by mean curvature, in radially symmetric
environments and for all directions. Correctors also exist and, hence,
homogenization holds for many directions for non convex Hamiltoni-ans and
general stationary ergodic media.
