Random Walks Associated with Non-Divergence Form Elliptic Equations

This paper is concerned with the study of the diffusion process associated with a nondivergence form elliptic operator in d dimensions, d => 2. The authors introduce a new technique for studying the diffusion, based on the observation that the probability of escape from a d -1 dimensional hyperplane can be explicitly calculated. They use the method to estimate the probability of escape from d -1 dimensional manifolds which are C 1, (alpha) , and also d–1 dimensional Lipschitz manifolds. To implement their method the authors study various random walks induced by the diffusion process, and compare them to the corresponding walks induced by Brownian motion.