  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.
