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.
|Name||Memorandum / Department of Applied Mathematics|
|Publisher||University of Twente, Department of Applied Mathematics|
- limiting conditional distribution
- Absorbing Markov chain
- Quasi-stationary distribution
- survival-time distribution
- death process