### Abstract

Original language | Undefined |
---|---|

Place of Publication | Enschede |

Publisher | University of Twente, Department of Applied Mathematics |

Number of pages | 14 |

Publication status | Published - Jan 2007 |

### Publication series

Name | Memorandum / Department of Applied Mathematics |
---|---|

Publisher | University of Twente, Department of Applied Mathematics |

No. | 1/1815 |

ISSN (Print) | 1874-4850 |

ISSN (Electronic) | 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

### Cite this

*Survival in a quasi-death process*. (Memorandum / Department of Applied Mathematics; No. 1/1815). Enschede: University of Twente, Department of Applied Mathematics.

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*Survival in a quasi-death process*. Memorandum / Department of Applied Mathematics, no. 1/1815, University of Twente, Department of Applied Mathematics, Enschede.

**Survival in a quasi-death process.** / van Doorn, Erik A.; Pollett, Philip K.

Research output: Book/Report › Report › Professional

TY - BOOK

T1 - Survival in a quasi-death process

AU - van Doorn, Erik A.

AU - Pollett, Philip K.

PY - 2007/1

Y1 - 2007/1

N2 - 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.

AB - 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.

KW - limiting conditional distribution

KW - MSC-60J27

KW - Absorbing Markov chain

KW - Quasi-stationary distribution

KW - EWI-8237

KW - survival-time distribution

KW - death process

KW - METIS-241734

KW - IR-66636

M3 - Report

T3 - Memorandum / Department of Applied Mathematics

BT - Survival in a quasi-death process

PB - University of Twente, Department of Applied Mathematics

CY - Enschede

ER -