IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v189y2011i1p63-10210.1007-s10479-009-0664-7.html
   My bibliography  Save this article

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

Author

Listed:
  • 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

Suggested Citation

  • 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
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10479-009-0664-7
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10479-009-0664-7?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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. 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.
    3. 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.
    4. 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.
    5. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    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.
    2. Kleijnen, Jack P.C. & Ridder, A.A.N. & Rubinstein, R.Y., 2010. "Variance Reduction Techniques in Monte Carlo Methods," Other publications TiSEM 87680d1a-53c1-4107-ada4-7, Tilburg University, School of Economics and Management.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. O. J. Boxma & E. J. Cahen & D. Koops & M. Mandjes, 2019. "Linear Stochastic Fluid Networks: Rare-Event Simulation and Markov Modulation," Methodology and Computing in Applied Probability, Springer, vol. 21(1), pages 125-153, March.
    8. Kontosakos, Vasileios E. & Mendonca, Keegan & Pantelous, Athanasios A. & Zuev, Konstantin M., 2021. "Pricing discretely-monitored double barrier options with small probabilities of execution," European Journal of Operational Research, Elsevier, vol. 290(1), pages 313-330.
    9. Kaynar, Bahar & Ridder, Ad, 2010. "The cross-entropy method with patching for rare-event simulation of large Markov chains," European Journal of Operational Research, Elsevier, vol. 207(3), pages 1380-1397, December.
    10. Tito Homem-de-Mello, 2007. "A Study on the Cross-Entropy Method for Rare-Event Probability Estimation," INFORMS Journal on Computing, INFORMS, vol. 19(3), pages 381-394, August.
    11. Paredes, R. & Dueñas-Osorio, L. & Meel, K.S. & Vardi, M.Y., 2019. "Principled network reliability approximation: A counting-based approach," Reliability Engineering and System Safety, Elsevier, vol. 191(C).
    12. Krystul, Jaroslav & Le Gland, François & Lezaud, Pascal, 2012. "Sampling per mode for rare event simulation in switching diffusions," Stochastic Processes and their Applications, Elsevier, vol. 122(7), pages 2639-2667.
    13. Michael B. Giles, 2008. "Multilevel Monte Carlo Path Simulation," Operations Research, INFORMS, vol. 56(3), pages 607-617, June.
    14. Paul Dupuis & Kevin Leder & Hui Wang, 2009. "Importance Sampling for Weighted-Serve-the-Longest-Queue," Mathematics of Operations Research, INFORMS, vol. 34(3), pages 642-660, August.
    15. Villén-Altamirano, José, 2010. "Importance functions for restart simulation of general Jackson networks," European Journal of Operational Research, Elsevier, vol. 203(1), pages 156-165, May.
    16. Lagnoux-Renaudie, Agnès, 2008. "Effective branching splitting method under cost constraint," Stochastic Processes and their Applications, Elsevier, vol. 118(10), pages 1820-1851, October.
    17. Fabian Dickmann & Nikolaus Schweizer, 2014. "Faster Comparison of Stopping Times by Nested Conditional Monte Carlo," Papers 1402.0243, arXiv.org.
    18. D.D. Riley & X. Koutsoukos, 2014. "Probabilistic verification of a biodiesel production system using statistical model checking," Mathematical and Computer Modelling of Dynamical Systems, Taylor & Francis Journals, vol. 20(5), pages 452-469, September.
    19. James Hodgson & Adam M. Johansen & Murray Pollock, 2022. "Unbiased Simulation of Rare Events in Continuous Time," Methodology and Computing in Applied Probability, Springer, vol. 24(3), pages 2123-2148, September.
    20. Pierre L'Ecuyer & Christian Lécot & Bruno Tuffin, 2008. "A Randomized Quasi-Monte Carlo Simulation Method for Markov Chains," Operations Research, INFORMS, vol. 56(4), pages 958-975, August.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:annopr:v:189:y:2011:i:1:p:63-102:10.1007/s10479-009-0664-7. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.