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Splitting for rare event simulation: A large deviation approach to design and analysis

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  • Dean, Thomas
  • Dupuis, Paul

Abstract

Particle splitting methods are considered for the estimation of rare events. The probability of interest is that a Markov process first enters a set B before another set A, and it is assumed that this probability satisfies a large deviation scaling. A notion of subsolution is defined for the related calculus of variations problem, and two main results are proved under mild conditions. The first is that the number of particles generated by the algorithm grows subexponentially if and only if a certain scalar multiple of the importance function is a subsolution. The second is that, under the same condition, the variance of the algorithm is characterized (asymptotically) in terms of the subsolution. The design of asymptotically optimal schemes is discussed, and numerical examples are presented.

Suggested Citation

  • Dean, Thomas & Dupuis, Paul, 2009. "Splitting for rare event simulation: A large deviation approach to design and analysis," Stochastic Processes and their Applications, Elsevier, vol. 119(2), pages 562-587, February.
    • Handle: RePEc:eee:spapps:v:119:y:2009:i:2:p:562-587
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    Citations

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    Cited by:

    1. Anne Buijsrogge & Pieter-Tjerk Boer & Werner R. W. Scheinhardt, 2019. "Importance sampling for non-Markovian tandem queues using subsolutions," Queueing Systems: Theory and Applications, Springer, vol. 93(1), pages 31-65, October.
    2. Fatma Başoğlu Kabran & Ali Devin Sezer, 2022. "Approximation of the exit probability of a stable Markov modulated constrained random walk," Annals of Operations Research, Springer, vol. 310(2), pages 431-475, March.
    3. Zdravko I. Botev & Pierre L’Ecuyer, 2020. "Sampling Conditionally on a Rare Event via Generalized Splitting," INFORMS Journal on Computing, INFORMS, vol. 32(4), pages 986-995, October.
    4. Thomas Dean & Paul Dupuis, 2011. "The design and analysis of a generalized RESTART/DPR algorithm for rare event simulation," Annals of Operations Research, Springer, vol. 189(1), pages 63-102, September.
    5. Jose Blanchet, 2013. "Optimal Sampling of Overflow Paths in Jackson Networks," Mathematics of Operations Research, INFORMS, vol. 38(4), pages 698-719, November.
    6. Kamil Demirberk Ünlü & Ali Devin Sezer, 2020. "Excessive backlog probabilities of two parallel queues," Annals of Operations Research, Springer, vol. 293(1), pages 141-174, October.
    7. Hult, Henrik & Nyquist, Pierre, 2016. "Large deviations for weighted empirical measures arising in importance sampling," Stochastic Processes and their Applications, Elsevier, vol. 126(1), pages 138-170.

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