Numerical Implementation of Finite-Time Shadowing of Stochastic Differential Equations

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.