IDEAS home Printed from https://ideas.repec.org/a/eee/reensy/v135y2015icp107-124.html
   My bibliography  Save this article

PC analysis of stochastic differential equations driven by Wiener noise

Author

Listed:
  • Le Maître, O.P.
  • Knio, O.M.

Abstract

A polynomial chaos (PC) analysis with stochastic expansion coefficients is proposed for stochastic differential equations driven by additive or multiplicative Wiener noise. It is shown that for this setting, a Galerkin formalism naturally leads to the definition of a hierarchy of stochastic differential equations governing the evolution of the PC modes. Under the mild assumption that the Wiener and uncertain parameters can be treated as independent random variables, it is also shown that the Galerkin formalism naturally separates parametric uncertainty and stochastic forcing dependences. This enables us to perform an orthogonal decomposition of the process variance, and consequently identify contributions arising from the uncertainty in parameters, the stochastic forcing, and a coupled term. Insight gained from this decomposition is illustrated in light of implementation to simplified linear and non-linear problems; the case of a stochastic bifurcation is also considered.

Suggested Citation

  • Le Maître, O.P. & Knio, O.M., 2015. "PC analysis of stochastic differential equations driven by Wiener noise," Reliability Engineering and System Safety, Elsevier, vol. 135(C), pages 107-124.
    • Handle: RePEc:eee:reensy:v:135:y:2015:i:c:p:107-124
    DOI: 10.1016/j.ress.2014.11.002
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0951832014002749
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ress.2014.11.002?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. Crestaux, Thierry & Le Maıˆtre, Olivier & Martinez, Jean-Marc, 2009. "Polynomial chaos expansion for sensitivity analysis," Reliability Engineering and System Safety, Elsevier, vol. 94(7), pages 1161-1172.
    2. Michael B. Giles, 2008. "Multilevel Monte Carlo Path Simulation," Operations Research, INFORMS, vol. 56(3), pages 607-617, June.
    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. Safa Alaskary & Mohamed El-Beltagy, 2020. "Uncertainty Quantification Spectral Technique for the Stochastic Point Reactor with Random Parameters," Energies, MDPI, vol. 13(6), pages 1-11, March.
    2. Pierre Étoré & Clémentine Prieur & Dang Khoi Pham & Long Li, 2020. "Global Sensitivity Analysis for Models Described by Stochastic Differential Equations," Methodology and Computing in Applied Probability, Springer, vol. 22(2), pages 803-831, June.

    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. Abgrall, R. & Congedo, P.M. & Geraci, G., 2017. "Towards a unified multiresolution scheme for treating discontinuities in differential equations with uncertainties," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 139(C), pages 1-22.
    2. Palar, Pramudita Satria & Zuhal, Lavi Rizki & Shimoyama, Koji & Tsuchiya, Takeshi, 2018. "Global sensitivity analysis via multi-fidelity polynomial chaos expansion," Reliability Engineering and System Safety, Elsevier, vol. 170(C), pages 175-190.
    3. Fabian Dickmann & Nikolaus Schweizer, 2014. "Faster Comparison of Stopping Times by Nested Conditional Monte Carlo," Papers 1402.0243, arXiv.org.
    4. Wang, Zihan & Daeipour, Mohamad & Xu, Hongyi, 2023. "Quantification and propagation of Aleatoric uncertainties in topological structures," Reliability Engineering and System Safety, Elsevier, vol. 233(C).
    5. Yi Chen & Jing Dong & Hao Ni, 2021. "ɛ-Strong Simulation of Fractional Brownian Motion and Related Stochastic Differential Equations," Mathematics of Operations Research, INFORMS, vol. 46(2), pages 559-594, May.
    6. Jian Wang & Xiang Gao & Zhili Sun, 2021. "A Multilevel Simulation Method for Time-Variant Reliability Analysis," Sustainability, MDPI, vol. 13(7), pages 1-16, March.
    7. Ahmed Kebaier & J'er^ome Lelong, 2015. "Coupling Importance Sampling and Multilevel Monte Carlo using Sample Average Approximation," Papers 1510.03590, arXiv.org, revised Jul 2017.
    8. Gayathri, P. & Umesh, K. & Ganguli, R., 2010. "Effect of matrix cracking and material uncertainty on composite plates," Reliability Engineering and System Safety, Elsevier, vol. 95(7), pages 716-728.
    9. Stéphane Crépey & Noufel Frikha & Azar Louzi & Gilles Pagès, 2023. "Asymptotic Error Analysis of Multilevel Stochastic Approximations for the Value-at-Risk and Expected Shortfall," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-04304985, HAL.
    10. Wei Fang & Zhenru Wang & Michael B. Giles & Chris H. Jackson & Nicky J. Welton & Christophe Andrieu & Howard Thom, 2022. "Multilevel and Quasi Monte Carlo Methods for the Calculation of the Expected Value of Partial Perfect Information," Medical Decision Making, , vol. 42(2), pages 168-181, February.
    11. Lay Harold A. & Colgin Zane & Reshniak Viktor & Khaliq Abdul Q. M., 2018. "On the implementation of multilevel Monte Carlo simulation of the stochastic volatility and interest rate model using multi-GPU clusters," Monte Carlo Methods and Applications, De Gruyter, vol. 24(4), pages 309-321, December.
    12. Hideyuki Tanaka & Toshihiro Yamada, 2012. "Strong Convergence for Euler-Maruyama and Milstein Schemes with Asymptotic Method," Papers 1210.0670, arXiv.org, revised Nov 2013.
    13. Nagy Shady Ahmed & Wafa Mohamed & El-Beltagy Mohamed A., 2020. "Multilevel Monte Carlo by using the Halton sequence," Monte Carlo Methods and Applications, De Gruyter, vol. 26(3), pages 193-203, September.
    14. F Bourgey & S de Marco & Emmanuel Gobet & Alexandre Zhou, 2020. "Multilevel Monte-Carlo methods and lower-upper bounds in Initial Margin computations," Post-Print hal-02430430, HAL.
    15. Lokman A. Abbas-Turki & Stéphane Crépey & Babacar Diallo, 2018. "Xva Principles, Nested Monte Carlo Strategies, And Gpu Optimizations," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(06), pages 1-40, September.
    16. Simonella, Roberta & Vázquez, Carlos, 2023. "XVA in a multi-currency setting with stochastic foreign exchange rates," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 207(C), pages 59-79.
    17. Hoel Håkon & Tempone Raúl & von Schwerin Erik & Szepessy Anders, 2014. "Implementation and analysis of an adaptive multilevel Monte Carlo algorithm," Monte Carlo Methods and Applications, De Gruyter, vol. 20(1), pages 1-41, March.
    18. Aintablian, Sebouh & Khoury, Wissam El, 2017. "A simulation on the presence of competing bidders in mergers and acquisitions," Finance Research Letters, Elsevier, vol. 22(C), pages 233-243.
    19. F Bourgey & S de Marco & Emmanuel Gobet & Alexandre Zhou, 2020. "Multilevel Monte-Carlo methods and lower-upper bounds in Initial Margin computations," Working Papers hal-02430430, HAL.
    20. 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.

    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:eee:reensy:v:135:y:2015:i:c:p:107-124. 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: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/reliability-engineering-and-system-safety .

    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.