Numerical Implementation of Finite-Time Shadowing of Stochastic Differential Equations

Qingyi Zhan (), Zhifang Zhang () and Yuhong Li ()
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Qingyi Zhan: Fujian Agriculture and Forestry University
Zhifang Zhang: Fujian Center for Disease Control and Prevention
Yuhong Li: Huazhong University of Science and Technology

Indian Journal of Pure and Applied Mathematics, 2020, vol. 51, issue 4, 1939-1957

Abstract: 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.

Keywords: Stochastic differential equations; random shadowing; numerical implementation; stochastic Chen system; 37H05; 37C50; 65C30; 65P20 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s13226-020-0506-5

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