Stochastic shadowing analysis of a class of stochastic differential equations

Volume 10, Issue 10, pp 5552--5565 http://dx.doi.org/10.22436/jnsa.010.10.35

Publication Date: October 31, 2017 Submission Date: January 26, 2017

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Authors

Qingyi Zhan - College of Computer and Information Science, Fujian Agriculture and Forestry University, Fuzhou, Fujian 350002, P. R. China. - Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, P. R. China. Yuhong Li - College of Hydropower and Information Engineering, Huazhong University of Science and Technology, Wuhan, 430074, P. R. China.

Abstract

This paper is devoted to the feasibility of stochastic shadowing of a class of stochastic differential equations via numerical analysis tools. A general shadowing theorem of stochastic differential equations is proven, and an explicit relationship of shadowing and the coefficients of SDE, a bound for shadowing distance are both investigated. The focus is explicit regularity conditions of stochastic differential equations which can ensure the shadowing. A numerical experiment is provided to illustrate the effectiveness of the proposed theorem by the numerical simulations of chaotic orbits of the stochastic Lorenz equations.

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Keywords

• Stochastic differential equations
• random dynamical systems
• numerical method
• shadowing
• multiplicative ergodic theorem
• stochastic Lorenz equations

MSC

•  65C20
•  65P20
•  37H10
•  37C50

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