Numerical study on (ω, Lδ)-Lipschitz shadowing of stochastic differential equations

Abstract This paper focuses on the feasibility and numerical implementations of (ω, Lδ)-Lipschitz shadowing of a class of stochastic differential equations via numerical analysis. A new notion of random Lipschitz shadowing and exact estimation of shadowing distance of stochastic differential equations are investigated. Moreover, the measurability of the true orbits is also studied. Numerical simulations of chaotic orbits of stochastic L u ¨ system are provided to illustrate the effectiveness of the proposed theorem.