IDEAS home Printed from https://ideas.repec.org/a/spr/jotpro/v35y2022i1d10.1007_s10959-020-01052-7.html
   My bibliography  Save this article

An Approximation Scheme for Reflected Stochastic Differential Equations with Non-Lipschitzian Coefficients

Author

Listed:
  • Junxia Duan

    (Central South University)

  • Jun Peng

    (Central South University)

Abstract

In this paper, we study a numerical approximation scheme for reflected stochastic differential equations (SDEs) with non-Lipschitzian coefficients in a bounded convex domain. It is shown, under some mild conditions, that the approximation scheme converges in uniform $${{L}}^2 $$ L 2 to the solution of reflected SDEs. Moreover, we move from local to global monotonicity conditions and consider the rate of convergence for our approximation scheme to reflected SDEs with coefficients which have at most polynomial growth.

Suggested Citation

  • Junxia Duan & Jun Peng, 2022. "An Approximation Scheme for Reflected Stochastic Differential Equations with Non-Lipschitzian Coefficients," Journal of Theoretical Probability, Springer, vol. 35(1), pages 575-602, March.
    • Handle: RePEc:spr:jotpro:v:35:y:2022:i:1:d:10.1007_s10959-020-01052-7
    DOI: 10.1007/s10959-020-01052-7
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10959-020-01052-7
    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/s10959-020-01052-7?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. Lan, Guangqiang & Wu, Jiang-Lun, 2014. "New sufficient conditions of existence, moment estimations and non confluence for SDEs with non-Lipschitzian coefficients," Stochastic Processes and their Applications, Elsevier, vol. 124(12), pages 4030-4049.
    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. Xu, Jie & Wen, Jiaping & Mu, Jianyong & Liu, Jicheng, 2019. "Stochastic flows of SDEs with non-Lipschitz coefficients and singular time," Statistics & Probability Letters, Elsevier, vol. 148(C), pages 118-127.
    2. Lan, Guangqiang & Xia, Fang & Zhao, Mei, 2020. "pth moment (p∈(0,1)) and almost sure exponential stability of the exact solutions and modified truncated EM method for stochastic differential equations," Statistics & Probability Letters, Elsevier, vol. 160(C).

    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:35:y:2022:i:1:d:10.1007_s10959-020-01052-7. 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.