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Conditioning an additive functional of a markov chain to stay nonnegative. II, Hitting a high level
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Jacka, Saul D., Lazic, Zorana and Warren, Jon (2005) Conditioning an additive functional of a markov chain to stay nonnegative. II, Hitting a high level. Advances in Applied Probability, Vol.37 (No.4). pp. 1035-1055. doi:10.1239/aap/1134587752 ISSN 0001-8678.
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Official URL: http://dx.doi.org/10.1239/aap/1134587752
Abstract
Let (X-t)(t >= 0) be a continuous-time irreducible Markov chain on a finite state space E, let v: E -> R \ {0}, and let (phi(t))(t >= 0) be defined by phi(t) = integral(0)(t) v(X-s) ds. We consider the case in which the process (phi(t))(t >= 0) is oscillating and that in which (phi(t))(t >= 0) has a negative drift. In each of these cases, we condition the process (X-t, phi(t))(t >= 0) on the event that (phi(t))(t >= 0) hits level y before hitting 0 and prove weak convergence of the conditioned process as y -> infinity. In addition, we show the relationship between the conditioning of the process (phi(t))(t >= 0) with a negative drift to oscillate and the conditioning of it to stay nonnegative for a long time, and the relationship between the conditioning of (phi(t))(t >= 0) with a negative drift to drift to infinity and the conditioning of it to hit large levels before hitting 0.
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | ||||
Library of Congress Subject Headings (LCSH): | Markov processes | ||||
Journal or Publication Title: | Advances in Applied Probability | ||||
Publisher: | Applied Probability Trust | ||||
ISSN: | 0001-8678 | ||||
Official Date: | December 2005 | ||||
Dates: |
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Volume: | Vol.37 | ||||
Number: | No.4 | ||||
Number of Pages: | 21 | ||||
Page Range: | pp. 1035-1055 | ||||
DOI: | 10.1239/aap/1134587752 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access |
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