Estimating Rare Event Probabilities in Large Scale Stochastic Hybrid Systems by Sequential Monte Carlo Simulation

H.A.P. Blom, J. Krystul, G.J. Bakker

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    15 Citations (Scopus)

    Abstract

    We study the problem of estimating small reachability probabilities for large scale stochastic hybrid processes through Sequential Monte Carlo (SMC) simulation. Recently, [Cerou et al., 2002, 2005] developed an SMC approach for diffusion processes, and referred to the resulting SMC algorithm as an Interacting Particle System (IPS). In [Krystul&Blom, 2004, 2005] it was shown that this IPS approach works very well for a diffusion example, but has its limits when applied to a switching diffusion with large differences in discrete state (mode) probabilities or with rare mode switching. In order to cope with these problems, in [Krystul&Blom, 2004, 2005, 2006] the IPS approach has been extended to Hybrid IPS (HIPS) versions. Unfortunately, these HIPS versions may need impractically many particles when the space of the discrete state component is very large. Such situation typically occurs when the stochastic process considered is highly distributed and incorporates many local discrete valued switching processes. Then the vector of local discrete valued components has a state space the size of which is exponentially large. The aim of the current work is formulate the estimation of extremely small rare event probabilities in stochastic hybrid systems with a large state space for the discrete valued process component into one of a hierarchical estimation process, and to use this for the derivation of a Hierarchical HIPS version. The effectiveness of the approach is illustrated for evaluating the risk of collision between two aircraft in a scenario of the future.
    Original languageUndefined
    Title of host publication6th International Workshop on Rare Event Simulation
    Place of PublicationBamberg
    PublisherUniversität Bamberg
    Pages1-7
    Number of pages7
    ISBN (Print)not assigned
    Publication statusPublished - 10 Oct 2006
    Event6th International Workshop on Rare Event Simulation, Bamberg, Germany: Proceedings of the 6th International Workshop on Rare Event Simulation -
    Duration: 1 Oct 2006 → …

    Publication series

    Name
    NumberA219

    Conference

    Conference6th International Workshop on Rare Event Simulation, Bamberg, Germany
    Period1/10/06 → …

    Keywords

    • EWI-9129
    • METIS-237928
    • IR-63927

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