Rates of convergence in periodic homogenization offully nonlinear uniformly elliptic PDEs

We consider periodic homogenization of the fully nonlinear uniformly elliptic equation u(epsilon) + H(x, x/epsilon, Du(epsilon), D(2)u(epsilon)) = 0. We give an estimate of the rate of convergence of u(epsilon) to the solution u of the homogenized problem u + H(x, Du, D(2)u) = 0. Moreover we describe a numerical scheme for the approximation of the effective nonlinearity H and we estimate the corresponding rate of convergence.