# Survival in a quasi-death process

Erik A. van Doorn, Philip K. Pollett

Research output: Book/ReportReportProfessional

## 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.
Original language Undefined Enschede University of Twente, Department of Applied Mathematics 14 Published - Jan 2007

### Publication series

Name Memorandum / Department of Applied Mathematics University of Twente, Department of Applied Mathematics 1/1815 1874-4850 1874-4850

## Keywords

• limiting conditional distribution
• MSC-60J27
• Absorbing Markov chain
• Quasi-stationary distribution
• EWI-8237
• survival-time distribution
• death process
• METIS-241734
• IR-66636