Discrete approximation of reflected Brownian motions by Markov chains on partitions of domains

Abstract

In this paper, we study discrete approximation of reflected Brownian motions on domains in Euclidean space. Our approximation is given by a sequence of Markov chains on partitions of the domain, where we allow uneven or random partitions. We provide sufficient conditions for the weak convergence of the Markov chains.

36 pages, 1 figure, accepted publication in Transactions of the American Mathematical Society