Periodic approximations of the ergodic constants in the stochastic homogenization of nonlinear second-order (degenerate) equations.

Summary We prove that the effective nonlinearities (ergodic constants) obtained in the stochastic homogenization of Hamilton-Jacobi, ''viscous'' Hamilton-Jacobi and nonlinear uniformly elliptic pde are approximated by the analogous quantities of appropriate ''periodizations'' of the equations. We also obtain an error estimate, when there is a rate of convergence for the stochastic homogenization.