the equation. Such subadditive structures have only been found, with the exception of the results in [@ATY1; @ATY2], in the case of convex or quasi-convex Hamiltonians and equations with linear diffusion terms. For this reason, a general qualitative theory of stochastic homogenization for equations with nonconvex Hamiltonians or quasilinear viscous terms has proved elusive. Indeed, even identifying a single example for which it can be proven that homogenization holds for a viscous equation with nonconvex or quasilinear structure has remained open until now.

In this paper, we propose a new strategy for obtaining qualitative homogenization results, based on the simple idea that the lack of a subadditive structure can be overcome by a quantitative approach. Rather than using soft arguments based on ergodic theorems, we assume a much stronger mixing assumption for the coefficients (a finite range of dependence condition) and attempt to prove more: homogenization with an explicit error estimate. The quantitative theory of stochastic homogenization for Hamilton-Jacobi equations originated in [@ACS] for first-order equations and in [@AC] for semi-linear viscous equations. The strategy here is to build on the techniques introduced in [@ACS; @AC] to handle more general equations. While the arguments in those papers seem to still 