IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v161y2019icp102-112.html
   My bibliography  Save this article

On the Euler–Maruyama scheme for SDEs with bounded variation and Hölder continuous coefficients

Author

Listed:
  • Ngo, Hoang-Long
  • Taguchi, Dai

Abstract

We consider the strong rate of convergence of the Euler–Maruyama approximation for stochastic differential equations with possibly discontinuous drift and Hölder continuous diffusion coefficient. In particular, we show that the rates obtained in some recent papers can be improved under an additional assumption that the diffusion coefficient is of bounded variation.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:matcom:v:161:y:2019:i:c:p:102-112
    DOI: 10.1016/j.matcom.2019.01.012
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475419300321
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2019.01.012?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. Hashimoto, Hiroya & Tsuchiya, Takahiro, 2018. "Stability problems for Cantor stochastic differential equations," Stochastic Processes and their Applications, Elsevier, vol. 128(1), pages 211-232.
    2. Kusuoka, Seiichiro, 2017. "Continuity and Gaussian two-sided bounds of the density functions of the solutions to path-dependent stochastic differential equations via perturbation," Stochastic Processes and their Applications, Elsevier, vol. 127(2), pages 359-384.
    3. 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.
    4. Jirô Akahori & Yuri Imamura, 2014. "On a symmetrization of diffusion processes," Quantitative Finance, Taylor & Francis Journals, vol. 14(7), pages 1211-1216, July.
    5. Menoukeu Pamen, Olivier & Taguchi, Dai, 2017. "Strong rate of convergence for the Euler–Maruyama approximation of SDEs with Hölder continuous drift coefficient," Stochastic Processes and their Applications, Elsevier, vol. 127(8), pages 2542-2559.
    6. Rainer Avikainen, 2009. "On irregular functionals of SDEs and the Euler scheme," Finance and Stochastics, Springer, vol. 13(3), pages 381-401, September.
    7. Remigijus Mikulevicius & Eckhard Platen, 1991. "Rate of Convergence of the Euler Approximation for Diffusion Processes," Published Paper Series 1991-3, Finance Discipline Group, UTS Business School, University of Technology, Sydney.
    Full references (including those not matched with items on IDEAS)

    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. Holland, Teodor, 2024. "On the weak rate of convergence for the Euler–Maruyama scheme with Hölder drift," Stochastic Processes and their Applications, Elsevier, vol. 174(C).
    2. 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).
    3. De Angelis, Tiziano & Germain, Maximilien & Issoglio, Elena, 2022. "A numerical scheme for stochastic differential equations with distributional drift," Stochastic Processes and their Applications, Elsevier, vol. 154(C), pages 55-90.
    4. Mikulevicius, Remigijus & Zhang, Changyong, 2011. "On the rate of convergence of weak Euler approximation for nondegenerate SDEs driven by Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 121(8), pages 1720-1748, August.
    5. Mackevičius, Vigirdas, 1997. "Convergence rate of Euler scheme for stochastic differential equations: Functionals of solutions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 44(2), pages 109-121.
    6. Taguchi, Dai & Tanaka, Akihiro, 2020. "Probability density function of SDEs with unbounded and path-dependent drift coefficient," Stochastic Processes and their Applications, Elsevier, vol. 130(9), pages 5243-5289.
    7. Hideyuki Tanaka & Toshihiro Yamada, 2012. "Strong Convergence for Euler-Maruyama and Milstein Schemes with Asymptotic Method," Papers 1210.0670, arXiv.org, revised Nov 2013.
    8. 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.
    9. Yuta Otsuki & Shotaro Yagishita, 2024. "Optimal reinsurance and investment via stochastic projected gradient method based on Malliavin calculus," Papers 2411.05417, arXiv.org.
    10. 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.
    11. Giulia Di Nunno & Anton Yurchenko-Tytarenko, 2022. "Sandwiched Volterra Volatility model: Markovian approximations and hedging," Papers 2209.13054, arXiv.org, revised Jul 2024.
    12. Yaskov, Pavel, 2019. "On pathwise Riemann–Stieltjes integrals," Statistics & Probability Letters, Elsevier, vol. 150(C), pages 101-107.
    13. Daphné Giorgi & Vincent Lemaire & Gilles Pagès, 2020. "Weak Error for Nested Multilevel Monte Carlo," Methodology and Computing in Applied Probability, Springer, vol. 22(3), pages 1325-1348, September.
    14. 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).
    15. Mike Giles & Lukasz Szpruch, 2012. "Multilevel Monte Carlo methods for applications in finance," Papers 1212.1377, arXiv.org.
    16. Dereich, Steffen & Heidenreich, Felix, 2011. "A multilevel Monte Carlo algorithm for Lévy-driven stochastic differential equations," Stochastic Processes and their Applications, Elsevier, vol. 121(7), pages 1565-1587, July.
    17. Umut Çetin & Julien Hok, 2024. "Speeding up the Euler scheme for killed diffusions," Finance and Stochastics, Springer, vol. 28(3), pages 663-707, July.
    18. Michael B. Giles & Kristian Debrabant & Andreas Ro{ss}ler, 2013. "Analysis of multilevel Monte Carlo path simulation using the Milstein discretisation," Papers 1302.4676, arXiv.org, revised Jun 2019.
    19. Bourgey Florian & De Marco Stefano & Gobet Emmanuel & Zhou Alexandre, 2020. "Multilevel Monte Carlo methods and lower–upper bounds in initial margin computations," Monte Carlo Methods and Applications, De Gruyter, vol. 26(2), pages 131-161, June.
    20. Akahori, Jirô & Fan, Jie Yen & Imamura, Yuri, 2023. "On the convergence order of a binary tree approximation of symmetrized diffusion processes," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 211(C), pages 263-277.

    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:matcom:v:161:y:2019:i:c:p:102-112. 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.journals.elsevier.com/mathematics-and-computers-in-simulation/ .

    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.