Numerical Study of Random Periodic Lipschitz Shadowing of Stochastic Differential Equations

Abstract

This paper is devoted to a new numerical approach for the possibility of(ω,Lδ)-periodic Lipschitz shadowing of a class of stochastic differential equations. The existence of(ω,Lδ)-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(ω,Lδ)-periodic Lipschitz shadowing orbits of the stochastic logistic equation.