Estimating the Probability of a Rare Event Over a Finite Time Horizon

Pieter-Tjerk de Boer, Pierre L'Ecuyer, Gerardo Rubino, Bruno Tuffin

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    Abstract

    We study an approximation for the zero-variance change of measure to estimate the probability of a rare event in a continuous-time Markov chain. The rare event occurs when the chain reaches a given set of states before some fixed time limit. The jump rates of the chain are expressed as functions of a rarity parameter in a way that the probability of the rare event goes to zero when the rarity parameter goes to zero, and the behavior of our estimators is studied in this asymptotic regime. After giving a general expression for the zero-variance change of measure in this situation, we develop an approximation of it via a power series and show that this approximation provides a bounded relative error when the rarity parameter goes to zero. We illustrate the performance of our approximation on small numerical examples of highly reliableMarkovian systems. We compare it to a previously proposed heuristic that combines forcing with balanced failure biaising. We also exhibit the exact zero-variance change of measure for these examples and compare it with these two approximations.
    Original languageUndefined
    Title of host publicationProceedings of the 2007 Winter Simulation Conference, WSC'07
    PublisherIEEE
    Pages403-411
    Number of pages9
    ISBN (Print)978-1-4244-1306-5
    DOIs
    Publication statusPublished - 9 Dec 2007
    Event2007 Winter Simulation Conference - Washington, United States
    Duration: 9 Dec 200712 Dec 2007

    Publication series

    Name
    PublisherIEEE
    Number7

    Conference

    Conference2007 Winter Simulation Conference
    Abbreviated titleWSC 2007
    CountryUnited States
    CityWashington
    Period9/12/0712/12/07

    Keywords

    • EWI-11671
    • METIS-245911
    • IR-62094

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