IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v145y2019icp133-140.html
   My bibliography  Save this article

Tamed Euler–Maruyama approximation for stochastic differential equations with locally Hölder continuous diffusion coefficients

Author

Listed:
  • Ngo, Hoang Long
  • Luong, Duc Trong

Abstract

We study the strong convergence of the tamed Euler–Maruyama approximation for stochastic differential equations whose coefficients superlinearly grow and diffusion coefficient is locally Hölder continuous.

Suggested Citation

  • Ngo, Hoang Long & Luong, Duc Trong, 2019. "Tamed Euler–Maruyama approximation for stochastic differential equations with locally Hölder continuous diffusion coefficients," Statistics & Probability Letters, Elsevier, vol. 145(C), pages 133-140.
    • Handle: RePEc:eee:stapro:v:145:y:2019:i:c:p:133-140
    DOI: 10.1016/j.spl.2018.09.006
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715218303055
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spl.2018.09.006?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. Ngo, Hoang-Long & Taguchi, Dai, 2017. "Strong convergence for the Euler–Maruyama approximation of stochastic differential equations with discontinuous coefficients," Statistics & Probability Letters, Elsevier, vol. 125(C), pages 55-63.
    2. Alfonsi, Aurélien, 2013. "Strong order one convergence of a drift implicit Euler scheme: Application to the CIR process," Statistics & Probability Letters, Elsevier, vol. 83(2), pages 602-607.
    3. Jean-Francois Chassagneux & Antoine Jacquier & Ivo Mihaylov, 2014. "An explicit Euler scheme with strong rate of convergence for financial SDEs with non-Lipschitz coefficients," Papers 1405.3561, arXiv.org, revised Apr 2016.
    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. Gao, Xiangyu & Liu, Yi & Wang, Yanxia & Yang, Hongfu & Yang, Maosong, 2021. "Tamed-Euler method for nonlinear switching diffusion systems with locally Hölder diffusion coefficients," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).

    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. C'onall Kelly & Gabriel J. Lord, 2021. "An adaptive splitting method for the Cox-Ingersoll-Ross process," Papers 2112.09465, arXiv.org, revised Feb 2023.
    2. Gao, Xiangyu & Wang, Jianqiao & Wang, Yanxia & Yang, Hongfu, 2022. "The truncated Euler–Maruyama method for CIR model driven by fractional Brownian motion," Statistics & Probability Letters, Elsevier, vol. 189(C).
    3. Andrei Cozma & Christoph Reisinger, 2017. "Strong order 1/2 convergence of full truncation Euler approximations to the Cox-Ingersoll-Ross process," Papers 1704.07321, arXiv.org, revised Oct 2018.
    4. Mario Hefter & Arnulf Jentzen, 2019. "On arbitrarily slow convergence rates for strong numerical approximations of Cox–Ingersoll–Ross processes and squared Bessel processes," Finance and Stochastics, Springer, vol. 23(1), pages 139-172, January.
    5. Kęstutis Kubilius & Aidas Medžiūnas, 2020. "Positive Solutions of the Fractional SDEs with Non-Lipschitz Diffusion Coefficient," Mathematics, MDPI, vol. 9(1), pages 1-14, December.
    6. Cui, Zhenyu & Kirkby, J. Lars & Nguyen, Duy, 2021. "Efficient simulation of generalized SABR and stochastic local volatility models based on Markov chain approximations," European Journal of Operational Research, Elsevier, vol. 290(3), pages 1046-1062.
    7. Gao, Xiangyu & Liu, Yi & Wang, Yanxia & Yang, Hongfu & Yang, Maosong, 2021. "Tamed-Euler method for nonlinear switching diffusion systems with locally Hölder diffusion coefficients," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
    8. Andrei Cozma & Christoph Reisinger, 2015. "Exponential integrability properties of Euler discretization schemes for the Cox-Ingersoll-Ross process," Papers 1601.00919, arXiv.org.
    9. Yifan Bai & Xing Huang, 2023. "Log-Harnack Inequality and Exponential Ergodicity for Distribution Dependent Chan–Karolyi–Longstaff–Sanders and Vasicek Models," Journal of Theoretical Probability, Springer, vol. 36(3), pages 1902-1921, September.
    10. Kęstutis Kubilius & Aidas Medžiūnas, 2022. "Pathwise Convergent Approximation for the Fractional SDEs," Mathematics, MDPI, vol. 10(4), pages 1-16, February.
    11. Peng, Ling & Kloeden, Peter E., 2021. "Time-consistent portfolio optimization," European Journal of Operational Research, Elsevier, vol. 288(1), pages 183-193.
    12. Nikolaos Halidias & Ioannis Stamatiou, 2015. "Approximating explicitly the mean reverting CEV process," Papers 1502.03018, arXiv.org, revised May 2015.
    13. Mouna Ben Derouich & Ahmed Kebaier, 2022. "The interpolated drift implicit Euler scheme Multilevel Monte Carlo method for pricing Barrier options and applications to the CIR and CEV models," Papers 2210.00779, arXiv.org.
    14. Jean-Francois Chassagneux & Antoine Jacquier & Ivo Mihaylov, 2014. "An explicit Euler scheme with strong rate of convergence for financial SDEs with non-Lipschitz coefficients," Papers 1405.3561, arXiv.org, revised Apr 2016.
    15. Ngo, Hoang-Long & Taguchi, Dai, 2019. "On the Euler–Maruyama scheme for SDEs with bounded variation and Hölder continuous coefficients," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 161(C), pages 102-112.
    16. Przybyłowicz, Paweł & Szölgyenyi, Michaela, 2021. "Existence, uniqueness, and approximation of solutions of jump-diffusion SDEs with discontinuous drift," Applied Mathematics and Computation, Elsevier, vol. 403(C).
    17. Andrei Cozma & Christoph Reisinger, 2017. "Strong convergence rates for Euler approximations to a class of stochastic path-dependent volatility models," Papers 1706.07375, arXiv.org, revised Oct 2018.
    18. Hong, Jialin & Huang, Chuying & Kamrani, Minoo & Wang, Xu, 2020. "Optimal strong convergence rate of a backward Euler type scheme for the Cox–Ingersoll–Ross model driven by fractional Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 130(5), pages 2675-2692.
    19. Blanka Horvath & Oleg Reichmann, 2018. "Dirichlet Forms and Finite Element Methods for the SABR Model," Papers 1801.02719, arXiv.org.
    20. Antoine Jacquier & Emma R. Malone & Mugad Oumgari, 2019. "Stacked Monte Carlo for option pricing," Papers 1903.10795, arXiv.org.

    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:stapro:v:145:y:2019:i:c:p:133-140. 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: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    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.