First Hitting Place Probabilities for a Discrete Version of the Ornstein-Uhlenbeck Process
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 h...
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| Format: | Article |
| Language: | English |
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Wiley
2009-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2009/909835 |
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| _version_ | 1832558260902690816 |
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| author | Mario Lefebvre Jean-Luc Guilbault |
| author_facet | Mario Lefebvre Jean-Luc Guilbault |
| author_sort | Mario Lefebvre |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-93089607487e416f8ef64bfb796b10fa |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2009-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-93089607487e416f8ef64bfb796b10fa2025-02-03T01:32:47ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252009-01-01200910.1155/2009/909835909835First Hitting Place Probabilities for a Discrete Version of the Ornstein-Uhlenbeck ProcessMario Lefebvre0Jean-Luc Guilbault1Département de Mathématiques et de Génie Industriel, École Polytechnique, C.P. 6079, Succursale Centre-ville, Montréal, QC, H3C 3A7, CanadaDépartement de Mathématiques et de Génie Industriel, École Polytechnique, C.P. 6079, Succursale Centre-ville, Montréal, QC, H3C 3A7, CanadaA 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.http://dx.doi.org/10.1155/2009/909835 |
| spellingShingle | Mario Lefebvre Jean-Luc Guilbault First Hitting Place Probabilities for a Discrete Version of the Ornstein-Uhlenbeck Process International Journal of Mathematics and Mathematical Sciences |
| title | First Hitting Place Probabilities for a Discrete Version of the Ornstein-Uhlenbeck Process |
| title_full | First Hitting Place Probabilities for a Discrete Version of the Ornstein-Uhlenbeck Process |
| title_fullStr | First Hitting Place Probabilities for a Discrete Version of the Ornstein-Uhlenbeck Process |
| title_full_unstemmed | First Hitting Place Probabilities for a Discrete Version of the Ornstein-Uhlenbeck Process |
| title_short | First Hitting Place Probabilities for a Discrete Version of the Ornstein-Uhlenbeck Process |
| title_sort | first hitting place probabilities for a discrete version of the ornstein uhlenbeck process |
| url | http://dx.doi.org/10.1155/2009/909835 |
| work_keys_str_mv | AT mariolefebvre firsthittingplaceprobabilitiesforadiscreteversionoftheornsteinuhlenbeckprocess AT jeanlucguilbault firsthittingplaceprobabilitiesforadiscreteversionoftheornsteinuhlenbeckprocess |