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The design and analysis of a generalized RESTART/DPR algorithm for rare event simulation

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  • Thomas Dean
  • Paul Dupuis

Abstract

We consider a general class of branching methods with killing for the estimation of rare events. The class includes a number of existing schemes, including RESTART and DPR (Direct Probability Redistribution). A method for the design and analysis is developed when the quantity of interest can be embedded in a sequence whose limit is determined by a large deviation principle. A notion of subsolution for the related calculus of variations problem is introduced, and two main results are proved. One is that the number of particles and the total work scales subexponentially in the large deviation parameter when the branching process is constructed according to a subsolution. The second is that the asymptotic performance of the schemes as measured by the variance of the estimate can be characterized in terms of the subsolution. Some examples are given to demonstrate the performance of the method. Copyright Springer Science+Business Media, LLC 2011

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  • 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.
    • Handle: RePEc:spr:annopr:v:189:y:2011:i:1:p:63-102:10.1007/s10479-009-0664-7
    DOI: 10.1007/s10479-009-0664-7
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    References listed on IDEAS

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    1. Villen-Altamirano, Jose, 2007. "Rare event RESTART simulation of two-stage networks," European Journal of Operational Research, Elsevier, vol. 179(1), pages 148-159, May.
    2. 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.
    3. Paul Glasserman & Philip Heidelberger & Perwez Shahabuddin & Tim Zajic, 1999. "Multilevel Splitting for Estimating Rare Event Probabilities," Operations Research, INFORMS, vol. 47(4), pages 585-600, August.
    4. Sezer, Ali Devin, 2009. "Importance sampling for a Markov modulated queuing network," Stochastic Processes and their Applications, Elsevier, vol. 119(2), pages 491-517, February.
    5. Paul Dupuis & Hui Wang, 2007. "Subsolutions of an Isaacs Equation and Efficient Schemes for Importance Sampling," Mathematics of Operations Research, INFORMS, vol. 32(3), pages 723-757, August.
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    Cited by:

    1. 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.

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