Hitting Time and Inverse Problems for Markov Chains

Abstract

Let W n be a simple Markov chain on the integers. Suppose that X n is a simple Markov chain on the integers whose transition probabilities coincide with those of W n off a finite set. We prove that there is an M > 0 such that the Markov chain W n and the joint distributions of the first hitting time and first hitting place of X n started at the origin for the sets {-M, M} and {-(M + 1), (M + 1)} algorithmically determine the transition probabilities of X n .