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

Abstract EN

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.