This paper is devoted to the existence of a true random periodic solution near the numerical approximate one for a kind of stochastic differential equations. A general finite-time random periodic shadowing theorem is proposed for the random dynamical systems generated by some stochastic differential equations under appropriate conditions and an estimate of shadowing distance via computable quantities is given. Application is demonstrated in the numerical simulations of random periodic orbits of the stochastic Lorenz system for certain given parameters.
Part of the book: Dynamical Systems