  We study random homogenization of second-order, degenerate and quasilinear
Hamilton-Jacobi equations which are positively homogeneous in the gradient.
Included are the equations of forced mean curvature motion and others
describing geometric motions of level sets as well as a large class of viscous,
non-convex Hamilton-Jacobi equations. The main results include the first proof
of qualitative stochastic homogenization for such equations. We also present
quantitative error estimates which give an algebraic rate of homogenization.
