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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
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    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.
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