This paper is concerned with the study of solutions to discrete parabolic
equations in divergence form with random coefficients, and their convergence to
solutions of a homogenized equation. It has previously been shown that if the
random environment is translational invariant and ergodic, then solutions of
the random equation converge under diffusive scaling to solutions of a
homogenized parabolic PDE.
We present a stochastic numerical method for solving fully non-linear free
boundary problems of parabolic type and provide a rate of convergence under
reasonable conditions on the non-linearity.