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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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
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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| Summary: | 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. |
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| ISSN: | 0161-1712 1687-0425 |