IDEAS home Printed from https://ideas.repec.org/a/spr/jotpro/v32y2019i2d10.1007_s10959-018-0854-9.html
   My bibliography  Save this article

Convergence Rate of Euler–Maruyama Scheme for SDEs with Hölder–Dini Continuous Drifts

Author

Listed:
  • Jianhai Bao

    (Swansea University)

  • Xing Huang

    (Tianjin University)

  • Chenggui Yuan

    (Swansea University)

Abstract

In this paper, we are concerned with convergence rate of Euler–Maruyama scheme for stochastic differential equations with Hölder–Dini continuous drifts. The key contributions are as follows: (i) by means of regularity of non-degenerate Kolmogrov equation, we investigate convergence rate of Euler–Maruyama scheme for a class of stochastic differential equations which allow the drifts to be Dini continuous and unbounded; (ii) by the aid of regularization properties of degenerate Kolmogrov equation, we discuss convergence rate of Euler–Maruyama scheme for a range of degenerate stochastic differential equations where the drifts are Hölder–Dini continuous of order $$\frac{2}{3}$$ 2 3 with respect to the first component and are merely Dini-continuous concerning the second component.

Suggested Citation

  • Jianhai Bao & Xing Huang & Chenggui Yuan, 2019. "Convergence Rate of Euler–Maruyama Scheme for SDEs with Hölder–Dini Continuous Drifts," Journal of Theoretical Probability, Springer, vol. 32(2), pages 848-871, June.
  • Handle: RePEc:spr:jotpro:v:32:y:2019:i:2:d:10.1007_s10959-018-0854-9
    DOI: 10.1007/s10959-018-0854-9
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10959-018-0854-9
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.

    File URL: https://libkey.io/10.1007/s10959-018-0854-9?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. Mattingly, J. C. & Stuart, A. M. & Higham, D. J., 2002. "Ergodicity for SDEs and approximations: locally Lipschitz vector fields and degenerate noise," Stochastic Processes and their Applications, Elsevier, vol. 101(2), pages 185-232, October.
    2. Zhang, Xicheng, 2010. "Stochastic flows and Bismut formulas for stochastic Hamiltonian systems," Stochastic Processes and their Applications, Elsevier, vol. 120(10), pages 1929-1949, September.
    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. Jianhai Bao & Xing Huang, 2022. "Approximations of McKean–Vlasov Stochastic Differential Equations with Irregular Coefficients," Journal of Theoretical Probability, Springer, vol. 35(2), pages 1187-1215, 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. Bao, Jianhai & Wang, Feng-Yu & Yuan, Chenggui, 2019. "Asymptotic Log-Harnack inequality and applications for stochastic systems of infinite memory," Stochastic Processes and their Applications, Elsevier, vol. 129(11), pages 4576-4596.
    2. Lemaire, Vincent, 2007. "An adaptive scheme for the approximation of dissipative systems," Stochastic Processes and their Applications, Elsevier, vol. 117(10), pages 1491-1518, October.
    3. Susanne Ditlevsen & Adeline Samson, 2019. "Hypoelliptic diffusions: filtering and inference from complete and partial observations," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 81(2), pages 361-384, April.
    4. Song, Renming & Xie, Longjie, 2020. "Well-posedness and long time behavior of singular Langevin stochastic differential equations," Stochastic Processes and their Applications, Elsevier, vol. 130(4), pages 1879-1896.
    5. Quentin Clairon & Adeline Samson, 2020. "Optimal control for estimation in partially observed elliptic and hypoelliptic linear stochastic differential equations," Statistical Inference for Stochastic Processes, Springer, vol. 23(1), pages 105-127, April.
    6. Qiu Lin & Ruisheng Qi, 2023. "Optimal Weak Order and Approximation of the Invariant Measure with a Fully-Discrete Euler Scheme for Semilinear Stochastic Parabolic Equations with Additive Noise," Mathematics, MDPI, vol. 12(1), pages 1-29, December.
    7. Gao, Shuaibin & Li, Xiaotong & Liu, Zhuoqi, 2023. "Stationary distribution of the Milstein scheme for stochastic differential delay equations with first-order convergence," Applied Mathematics and Computation, Elsevier, vol. 458(C).
    8. ur Rahman, Ghaus & Badshah, Qaisar & Agarwal, Ravi P. & Islam, Saeed, 2021. "Ergodicity & dynamical aspects of a stochastic childhood disease model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 182(C), pages 738-764.
    9. Casella, Bruno & Roberts, Gareth O. & Stramer, Osnat, 2011. "Stability of Partially Implicit Langevin Schemes and Their MCMC Variants," MPRA Paper 95220, University Library of Munich, Germany.
    10. Jianhai Bao & Feng‐Yu Wang & Chenggui Yuan, 2020. "Ergodicity for neutral type SDEs with infinite length of memory," Mathematische Nachrichten, Wiley Blackwell, vol. 293(9), pages 1675-1690, September.
    11. Gadat, Sébastien & Panloup, Fabien & Saadane, Sofiane, 2016. "Stochastic Heavy Ball," TSE Working Papers 16-712, Toulouse School of Economics (TSE).
    12. Uda, Kenneth, 2019. "Ergodicity and spike rate for stochastic FitzHugh–Nagumo neural model with periodic forcing," Chaos, Solitons & Fractals, Elsevier, vol. 123(C), pages 383-399.
    13. Feng-Yu Wang, 2014. "Derivative Formula and Gradient Estimates for Gruschin Type Semigroups," Journal of Theoretical Probability, Springer, vol. 27(1), pages 80-95, March.
    14. Wujun Lv & Xing Huang, 2021. "Harnack and Shift Harnack Inequalities for Degenerate (Functional) Stochastic Partial Differential Equations with Singular Drifts," Journal of Theoretical Probability, Springer, vol. 34(2), pages 827-851, June.
    15. Bao, Jianhai & Wang, Jian, 2022. "Coupling approach for exponential ergodicity of stochastic Hamiltonian systems with Lévy noises," Stochastic Processes and their Applications, Elsevier, vol. 146(C), pages 114-142.
    16. Shu, Huisheng & Jiang, Ziwei & Zhang, Xuekang, 2023. "Parameter estimation for integrated Ornstein–Uhlenbeck processes with small Lévy noises," Statistics & Probability Letters, Elsevier, vol. 199(C).
    17. Xiliang Fan, 2019. "Derivative Formulas and Applications for Degenerate Stochastic Differential Equations with Fractional Noises," Journal of Theoretical Probability, Springer, vol. 32(3), pages 1360-1381, September.
    18. Cai, Yongli & Kang, Yun & Wang, Weiming, 2017. "A stochastic SIRS epidemic model with nonlinear incidence rate," Applied Mathematics and Computation, Elsevier, vol. 305(C), pages 221-240.
    19. Birrell, Jeremiah & Herzog, David P. & Wehr, Jan, 2012. "The transition from ergodic to explosive behavior in a family of stochastic differential equations," Stochastic Processes and their Applications, Elsevier, vol. 122(4), pages 1519-1539.
    20. Uda, Kenneth, 2021. "Averaging principle for stochastic differential equations in the random periodic regime," Stochastic Processes and their Applications, Elsevier, vol. 139(C), pages 1-36.

    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:jotpro:v:32:y:2019:i:2:d:10.1007_s10959-018-0854-9. 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.