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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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:	Date Event December 2005 Published
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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