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

Mario Lefebvre and Jean-Luc Guilbault

Article (2009)

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Cite this document: 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, p. 1-12. doi:10.1155/2009/909835
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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.

Open Access document in PolyPublie
Subjects: 2950 Mathématiques appliquées > 2950 Mathématiques appliquées
3000 Statistique et probabilité > 3000 Statistique et probabilité
3000 Statistique et probabilité > 3007 Processus stochastiques
Department: Département de mathématiques et de génie industriel
Research Center: Non applicable
Funders: CRSNG / NSERC
Date Deposited: 18 Jul 2019 14:45
Last Modified: 19 Jul 2019 01:20
PolyPublie URL: https://publications.polymtl.ca/3655/
Document issued by the official publisher
Journal Title: International Journal of Mathematics and Mathematical Sciences (vol. 2009)
Publisher: Hindawi
Official URL: https://doi.org/10.1155/2009/909835

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