First Hitting Place Probabilities for a Discrete Version of the Ornstein-Uhlenbeck Process. (25th November 2009) - Lefebvre, Mario; Guilbault, Jean-Luc
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 p i, i + 1 are not necessarily the same when i is positive and i is negative.