Quasi-stationary distributions

Erik A. van Doorn, Philip K. Pollett

    Research output: Book/ReportReportProfessional

    498 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.