The expected time till absorption when absorption is not certain

D.M. Walker

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.

AMS 1991 Subject Classification: Primary 60J27, Secondary 60J35

Keywords: Q-processes; invariant vectors; absorption times

Acknowledgement: This worked was funded by the Australian Research Council.

The authors:

• David Walker, Discipline of Mathematics, The University of Queensland. dmw@maths.uq.edu.au

Back to Research Communications

Back to PKP's home page

Last modified: 28th April 1997