### Abstract

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

Place of Publication | Enschede |

Publisher | University of Twente, Department of Applied Mathematics |

Number of pages | 64 |

Publication status | Published - Jun 2011 |

### Publication series

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

Publisher | University of Twente, Department of Applied Mathematics |

No. | 1945 |

ISSN (Print) | 1874-4850 |

ISSN (Electronic) | 1874-4850 |

### Keywords

- Applied probability
- Markov Processes
- IR-77521
- METIS-277669
- EWI-20245

### Cite this

*Quasi-stationary distributions*. (Memorandum / Department of Applied Mathematics; No. 1945). Enschede: University of Twente, Department of Applied Mathematics.

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*Quasi-stationary distributions*. Memorandum / Department of Applied Mathematics, no. 1945, University of Twente, Department of Applied Mathematics, Enschede.

**Quasi-stationary distributions.** / van Doorn, Erik A.; Pollett, Philip K.

Research output: Book/Report › Report › Professional

TY - BOOK

T1 - Quasi-stationary distributions

AU - van Doorn, Erik A.

AU - Pollett, Philip K.

PY - 2011/6

Y1 - 2011/6

N2 - This paper contains a survey of results related to quasi-stationary distributions, which arise in the setting of stochastic dynamical systems that eventually evanesce, and which may be useful in describing the long-term behaviour of such systems before evanescence. We are concerned mainly with continuous-time Markov chains over a finite or countably infinite state space, since these processes most often arise in applications, but will make reference to results for other processes where appropriate. Next to giving an historical account of the subject, we review the most important results on the existence and identification of quasi-stationary distributions for general Markov chains, and give special attention to birth-death processes and related models. Results on the question of whether a quasi-stationary distribution, given its existence, is indeed a good descriptor of the long-term behaviour of a system before evanescence, are reviewed as well. The paper is concluded with a summary of recent developments in numerical and approximation methods.

AB - This paper contains a survey of results related to quasi-stationary distributions, which arise in the setting of stochastic dynamical systems that eventually evanesce, and which may be useful in describing the long-term behaviour of such systems before evanescence. We are concerned mainly with continuous-time Markov chains over a finite or countably infinite state space, since these processes most often arise in applications, but will make reference to results for other processes where appropriate. Next to giving an historical account of the subject, we review the most important results on the existence and identification of quasi-stationary distributions for general Markov chains, and give special attention to birth-death processes and related models. Results on the question of whether a quasi-stationary distribution, given its existence, is indeed a good descriptor of the long-term behaviour of a system before evanescence, are reviewed as well. The paper is concluded with a summary of recent developments in numerical and approximation methods.

KW - Applied probability

KW - Markov Processes

KW - IR-77521

KW - METIS-277669

KW - EWI-20245

M3 - Report

T3 - Memorandum / Department of Applied Mathematics

BT - Quasi-stationary distributions

PB - University of Twente, Department of Applied Mathematics

CY - Enschede

ER -