First Hitting Place Probabilities for a Discrete Version of the Ornstein-Uhlenbeck Process. (25th November 2009)

• Record Type: Journal Article
• Authors: Lefebvre, Mario; Guilbault, Jean-Luc
• Other Names: Schechtman Gideon Academic Editor.
• Is Part Of: International journal of mathematics and mathematical sciences. Volume 2009(2009)
• Publication Date: 2009-11-25
• Subjects: Mathematics -- Periodicals; 510.5
• DOI: 10.1155/2009/909835
• Languages: English
• ISSNs: 0161-1712

Abstract

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.