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Conditioning an additive functional of a markov chain to stay non-negative. I, Survival for a long time

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Jacka, Saul D., Lazic, Zorana and Warren, Jon (2005) Conditioning an additive functional of a markov chain to stay non-negative. I, Survival for a long time. Advances in Applied Probability, Vol.37 (No.4). pp. 1015-1034. doi:10.1239/aap/1134587751

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Official URL: http://dx.doi.org/10.1239/aap/1134587751

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Abstract

Let (X-t)(t >= 0) be a continuous-time irreducible Markov chain on a finite state space E, let v be a map v: E -> R \ {0}, and let (phi(t))(t >= 0) be an additive functional defined by phi(t) = integral(0)(t)(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) is nonnegative until time T and prove weak convergence of the conditioned process as T -> infinity.

Item Type: Journal Article
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:
DateEvent
December 2005Published
Volume: Vol.37
Number: No.4
Number of Pages: 20
Page Range: pp. 1015-1034
DOI: 10.1239/aap/1134587751
Status: Peer Reviewed
Publication Status: Published
Access rights to Published version: Restricted or Subscription Access

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