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The expected time until absorption when absorption is not certain

Part of: Markov processes

Published online by Cambridge University Press:  14 July 2016

D. M. Walker
D. M. Walker*
Affiliation:
The University of Queensland
*
∗Postal address: Department of Mathematics, The University of Queensland, QLD 4072, Australia. Email address: [email protected].
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Abstract

This paper considers continuous-time Markov chains whose state space consists of an irreducible class, 𝒞, and an absorbing state which is accessible from 𝒞. The purpose is to provide a way to determine the expected time to absorption conditional on such time being finite, in the case where absorption occurs with probability less than 1. The results are illustrated by applications to the general birth and death process and the linear birth, death and catastrophe process.

Keywords

Q-processesinvariant vectorsabsorption times

MSC classification

Primary: 60J27: Continuous-time Markov processes on discrete state spaces
Secondary: 60J35: Transition functions, generators and resolvents
Type
Research Papers
Information
Journal of Applied Probability , Volume 35 , Issue 4 , December 1998 , pp. 812 - 823
Copyright
Copyright © Applied Probability Trust 1998 

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