AbstractIn this talk we consider the stochastic homogenization of elliptic non-divergence form equations on the integer lattice and the corresponding model of random walks in random environment (RWRE) which is a martingale. We will derive the optimal rates of the homogenization for the Dirichlet problem. We will also discuss the correlation structure of the invariant measure and quantitative es...
AbstractWe study the homogenization of the PDE $-A(x/\varepsilon):D^2 u_{\varepsilon} = f$ posed in a bounded convex domain subject to a Dirichlet boundary condition and the numerical approximation of the homogenized problem, where the measurable, uniformly elliptic, periodic and symmetric diffusion matrix $A$ is merely assumed to be essentially bounded and (in dimension $n>2$) to satisfy the C...