Quasi-stationary distributions

Erik A. van Doorn, Philip K. Pollett

Research output: Book/ReportReportProfessional

376 Downloads (Pure)

Abstract

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.
Original languageUndefined
Place of PublicationEnschede
PublisherUniversity of Twente, Department of Applied Mathematics
Number of pages64
Publication statusPublished - Jun 2011

Publication series

NameMemorandum / Department of Applied Mathematics
PublisherUniversity 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

van Doorn, E. A., & Pollett, P. K. (2011). Quasi-stationary distributions. (Memorandum / Department of Applied Mathematics; No. 1945). Enschede: University of Twente, Department of Applied Mathematics.
van Doorn, Erik A. ; Pollett, Philip K. / Quasi-stationary distributions. Enschede : University of Twente, Department of Applied Mathematics, 2011. 64 p. (Memorandum / Department of Applied Mathematics; 1945).
@book{3b2203a92f6d4a5b89f28579165c4098,
title = "Quasi-stationary distributions",
abstract = "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.",
keywords = "Applied probability, Markov Processes, IR-77521, METIS-277669, EWI-20245",
author = "{van Doorn}, {Erik A.} and Pollett, {Philip K.}",
year = "2011",
month = "6",
language = "Undefined",
series = "Memorandum / Department of Applied Mathematics",
publisher = "University of Twente, Department of Applied Mathematics",
number = "1945",

}

van Doorn, EA & Pollett, PK 2011, 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.

Enschede : University of Twente, Department of Applied Mathematics, 2011. 64 p. (Memorandum / Department of Applied Mathematics; No. 1945).

Research output: Book/ReportReportProfessional

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 -

van Doorn EA, Pollett PK. Quasi-stationary distributions. Enschede: University of Twente, Department of Applied Mathematics, 2011. 64 p. (Memorandum / Department of Applied Mathematics; 1945).