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Discrete Dynamics in Nature and Society
Volume 2018, Article ID 1967508, 10 pages
https://doi.org/10.1155/2018/1967508
Research Article

Numerical Study of Random Periodic Lipschitz Shadowing of Stochastic Differential Equations

1College of Computer and Information Science, Fujian Agriculture and Forestry University, Fuzhou 350002, China
2Ningde Normal University, Ningde, Fujian 352100, China

Correspondence should be addressed to Qingyi Zhan; nc.ca.cc.cesl@yqnahz

Received 10 July 2017; Accepted 10 October 2017; Published 11 January 2018

Academic Editor: Josef Diblik

Copyright © 2018 Qingyi Zhan and Xiangdong Xie. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper is devoted to a new numerical approach for the possibility of -periodic Lipschitz shadowing of a class of stochastic differential equations. The existence of -periodic Lipschitz shadowing orbits and expression of shadowing distance are established. The numerical implementation approaches to the shadowing distance by the random Romberg algorithm are presented, and the convergence of this method is also proved to be mean-square. This ensures the feasibility of the numerical method. The practical use of these theorems and the associated algorithms is demonstrated in the numerical computations of the -periodic Lipschitz shadowing orbits of the stochastic logistic equation.