### Abstract

Original language | English |
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Place of Publication | Enschede |

Publisher | University of Twente, Department of Applied Mathematics |

Number of pages | 22 |

Publication status | Published - 2004 |

### Publication series

Name | Memorandum Faculty of Mathematical Sciences |
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Publisher | University of Twente, Department of Applied Mathematics |

No. | 1737 |

ISSN (Print) | 0169-2690 |

### Fingerprint

### Keywords

- MSC-60J10
- EWI-3557
- METIS-219033
- IR-65921
- MSC-60J80

### Cite this

*Quasi-stationary distributions for a class of discrete-time Markov chains*. (Memorandum Faculty of Mathematical Sciences; No. 1737). Enschede: University of Twente, Department of Applied Mathematics.

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*Quasi-stationary distributions for a class of discrete-time Markov chains*. Memorandum Faculty of Mathematical Sciences, no. 1737, University of Twente, Department of Applied Mathematics, Enschede.

**Quasi-stationary distributions for a class of discrete-time Markov chains.** / Coolen-Schrijner, P.; van Doorn, E.A.

Research output: Book/Report › Report › Professional

TY - BOOK

T1 - Quasi-stationary distributions for a class of discrete-time Markov chains

AU - Coolen-Schrijner, P.

AU - van Doorn, E.A.

N1 - Imported from MEMORANDA

PY - 2004

Y1 - 2004

N2 - This paper is concerned with the circumstances under which a discrete-time absorbing Markov chain has a quasi-stationary distribution. We showed in a previous paper that a pure birth-death process with an absorbing bottom state has a quasi-stationary distribution -- actually an infinite family of quasi-stationary distributions -- if and only if absorption is certain and the chain is geometrically transient. If we widen the setting by allowing absorption in one step ({\it killing}) from any state, the two conditions are still necessary, but no longer sufficient. We show that the birth-death-type of behaviour prevails as long as the number of states in which killing can occur is finite. But if there are infinitely many such states, and if the chain is geometrically transient and absorption certain, then there may be 0, 1, or infinitely many quasi-stationary distributions. Examples of each type of behaviour are presented. We also survey and supplement the theory of quasi-stationary distributions for discrete-time Markov chains in general.

AB - This paper is concerned with the circumstances under which a discrete-time absorbing Markov chain has a quasi-stationary distribution. We showed in a previous paper that a pure birth-death process with an absorbing bottom state has a quasi-stationary distribution -- actually an infinite family of quasi-stationary distributions -- if and only if absorption is certain and the chain is geometrically transient. If we widen the setting by allowing absorption in one step ({\it killing}) from any state, the two conditions are still necessary, but no longer sufficient. We show that the birth-death-type of behaviour prevails as long as the number of states in which killing can occur is finite. But if there are infinitely many such states, and if the chain is geometrically transient and absorption certain, then there may be 0, 1, or infinitely many quasi-stationary distributions. Examples of each type of behaviour are presented. We also survey and supplement the theory of quasi-stationary distributions for discrete-time Markov chains in general.

KW - MSC-60J10

KW - EWI-3557

KW - METIS-219033

KW - IR-65921

KW - MSC-60J80

M3 - Report

T3 - Memorandum Faculty of Mathematical Sciences

BT - Quasi-stationary distributions for a class of discrete-time Markov chains

PB - University of Twente, Department of Applied Mathematics

CY - Enschede

ER -