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.