IDEAS home Printed from https://ideas.repec.org/a/spr/indpam/v51y2020i4d10.1007_s13226-020-0506-5.html
   My bibliography  Save this article

Numerical Implementation of Finite-Time Shadowing of Stochastic Differential Equations

Author

Listed:
  • Qingyi Zhan

    (Fujian Agriculture and Forestry University
    Illinois Institute of Technology)

  • Zhifang Zhang

    (Fujian Center for Disease Control and Prevention)

  • Yuhong Li

    (Huazhong University of Science and Technology)

Abstract

This paper focuses on the numerical implementation methods of shadowing theorem of stochastic differential equations. A general shadowing theorem of stochastic differential equations is given, and an explicit bound for shadowing distance is investigated. The main part is numerical implementation methods for shadowing distance in details. Numerical experiments are provided to illustrate the effectiveness of the proposed theorem by the numerical simulations of chaotic orbits of stochastic differential equations.

Suggested Citation

  • Qingyi Zhan & Zhifang Zhang & Yuhong Li, 2020. "Numerical Implementation of Finite-Time Shadowing of Stochastic Differential Equations," Indian Journal of Pure and Applied Mathematics, Springer, vol. 51(4), pages 1939-1957, December.
  • Handle: RePEc:spr:indpam:v:51:y:2020:i:4:d:10.1007_s13226-020-0506-5
    DOI: 10.1007/s13226-020-0506-5
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s13226-020-0506-5
    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/s13226-020-0506-5?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. Wang, Xiao & Duan, Jinqiao & Li, Xiaofan & Luan, Yuanchao, 2015. "Numerical methods for the mean exit time and escape probability of two-dimensional stochastic dynamical systems with non-Gaussian noises," Applied Mathematics and Computation, Elsevier, vol. 258(C), pages 282-295.
    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. Duan, Wei-Long & Zeng, Chunhua, 2017. "Signal power amplification of intracellular calcium dynamics with non-Gaussian noises and time delay," Applied Mathematics and Computation, Elsevier, vol. 292(C), pages 400-405.
    2. Qingyi Zhan & Zhifang Zhang & Yuhong Li, 2021. "Numerical implementation of finite-time shadowing of stochastic differential equations," Indian Journal of Pure and Applied Mathematics, Springer, vol. 52(4), pages 945-960, December.
    3. Zhan, Qingyi & Duan, Jinqiao & Li, Xiaofan & Li, Yuhong, 2024. "Symplectic numerical integration for Hamiltonian stochastic differential equations with multiplicative Lévy noise in the sense of Marcus," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 215(C), pages 420-439.
    4. Wang, Xiao & Duan, Jinqiao & Li, Xiaofan & Song, Renming, 2018. "Numerical algorithms for mean exit time and escape probability of stochastic systems with asymmetric Lévy motion," Applied Mathematics and Computation, Elsevier, vol. 337(C), pages 618-634.

    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:indpam:v:51:y:2020:i:4:d:10.1007_s13226-020-0506-5. 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.