Stochastic shadowing analysis of a class of stochastic differential equations

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.