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

Mario Lefebvre, Jean-Luc Guilbault

Article (2009)

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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,i1 are not necessarily the same when i is positive and i is negative.
Subjects: 2950 Applied mathematics > 2950 Applied mathematics
3000 Statistics and probability > 3000 Statistics and probability
3000 Statistics and probability > 3007 Stochastic processes
Department: Department of Mathematics and Industrial Engineering
Funders: CRSNG / NSERC
PolyPublie URL: https://publications.polymtl.ca/3655/
Journal Title: International Journal of Mathematics and Mathematical Sciences (vol. 2009)
Publisher: Hindawi
DOI: 10.1155/2009/909835
Official URL: https://doi.org/10.1155/2009/909835
Date Deposited: 18 Jul 2019 14:45
Last Modified: 11 Nov 2022 14:25
Cite in APA 7: Lefebvre, M., & Guilbault, J.-L. (2009). First hitting place probabilities for a discrete version of the Ornstein-Uhlenbeck Process. International Journal of Mathematics and Mathematical Sciences, 2009, 1-12. https://doi.org/10.1155/2009/909835

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