IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v414y2022ics0096300321007645.html
   My bibliography  Save this article

Convergence and stability of the semi-tamed Milstein method for commutative stochastic differential equations with non-globally Lipschitz continuous coefficients

Author

Listed:
  • Liu, Yulong
  • Niu, Yuanling
  • Cheng, Xiujun

Abstract

A new explicit stochastic scheme of order 1 is proposed for solving commutative stochastic differential equations (SDEs) with non-globally Lipschitz continuous coefficients. The proposed method is a semi-tamed version of Milstein scheme to solve SDEs with the drift coefficient consisting of non-Lipschitz continuous term and globally Lipschitz continuous term. It is easily implementable and achieves higher strong convergence order. A stability criterion for this method is derived, which shows that the stability condition of the numerical methods and that of the solved equations keep uniform. Compared with some widely used numerical schemes, the proposed method has better performance in inheriting the mean square stability of the exact solution of SDEs. Numerical experiments are given to illustrate the obtained convergence and stability properties.

Suggested Citation

  • Liu, Yulong & Niu, Yuanling & Cheng, Xiujun, 2022. "Convergence and stability of the semi-tamed Milstein method for commutative stochastic differential equations with non-globally Lipschitz continuous coefficients," Applied Mathematics and Computation, Elsevier, vol. 414(C).
  • Handle: RePEc:eee:apmaco:v:414:y:2022:i:c:s0096300321007645
    DOI: 10.1016/j.amc.2021.126680
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300321007645
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.amc.2021.126680?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. Yao, Jinran & Gan, Siqing, 2018. "Stability of the drift-implicit and double-implicit Milstein schemes for nonlinear SDEs," Applied Mathematics and Computation, Elsevier, vol. 339(C), pages 294-301.
    2. Zhang, Wei & Yin, Xunbo & Song, M.H. & Liu, M.Z., 2019. "Convergence rate of the truncated Milstein method of stochastic differential delay equations," Applied Mathematics and Computation, Elsevier, vol. 357(C), pages 263-281.
    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. Liu, Yufen & Cao, Wanrong & Li, Yuelin, 2022. "Split-step balanced θ-method for SDEs with non-globally Lipschitz continuous coefficients," Applied Mathematics and Computation, Elsevier, vol. 413(C).
    2. Xuewen Tan & Pengpeng Liu & Wenhui Luo & Hui Chen, 2022. "Analysis of a Class of Predation-Predation Model Dynamics with Random Perturbations," Mathematics, MDPI, vol. 10(18), pages 1-12, September.
    3. Arenas-López, J. Pablo & Badaoui, Mohamed, 2020. "The Ornstein-Uhlenbeck process for estimating wind power under a memoryless transformation," Energy, Elsevier, vol. 213(C).
    4. Bao, Zhenyu & Tang, Jingwen & Shen, Yan & Liu, Wei, 2021. "Equivalence of pth moment stability between stochastic differential delay equations and their numerical methods," Statistics & Probability Letters, Elsevier, vol. 168(C).
    5. Arenas-López, J. Pablo & Badaoui, Mohamed, 2020. "Stochastic modelling of wind speeds based on turbulence intensity," Renewable Energy, Elsevier, vol. 155(C), pages 10-22.

    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:apmaco:v:414:y:2022:i:c:s0096300321007645. 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/applied-mathematics-and-computation .

    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.