International Journal of Mathematics and Mathematical Sciences
Volume 2009 (2009), Article ID 909835, 12 pages
doi:10.1155/2009/909835

First hitting place probabilities for a discrete version of the Ornstein-Uhlenbeck process

Abstract

A Markov chain with state space {0,…,N} and transition probabilities depending on the current state is studied. The chain can be considered as a discrete Ornstein-Uhlenbeck process. The probability that the process hits N before 0 is computed explicitly. Similarly, the probability that the process hits N before −M is computed in the case when the state space is {−M,…,0,…,N} and the transition probabilities pi,i+1 are not necessarily the same when i is positive and i is negative.