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8237 Survival in a quasi-death process

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van Doorn, E.A. (2007) Survival in a quasi-death process. Memorandum 1815, Department of Applied Mathematics, University of Twente, Enschede. ISSN 1874-4850

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Official URL: http://www.math.utwente.nl/publications

Abstract

We consider a Markov chain in continuous time with an absorbing coffin state and a finite set $S$ of transient states. When $S$ is irreducible the limiting distribution of the chain as $t \to\infty,$ conditional on survival up to time $t,$ is known to equal the (unique) quasi-stationary distribution of the chain. We address the problem of generalizing this result to a setting in which $S$ may be reducible, and obtain a complete solution if the eigenvalue with maximal real part of the generator of the (sub)Markov chain on $S$ has multiplicity one. The result is applied to pure death processes and, more generally, to quasi-death processes.

Item Type:	Internal Report (Memorandum)
Research Group:	EWI-SP: Statistics and Probability
Research Program:	CTIT-IE&ICT: Industrial Engineering and ICT
Uncontrolled Keywords:	absorbing Markov chain, death process, limiting conditional distribution, quasi-stationary distribution, survival-time distribution
ID Code:	8237
Deposited On:	17 October 2007
More Information:	statistics metis

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Survival in a quasi-death process (deposited 17 October 2007)
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