First Hitting Place Probabilities for a Discrete Version of the Ornstein-Uhlenbeck Process.

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. [ABSTRACT FROM AUTHOR]