Numerical Approximation of Stochastic Theta Method for Random Periodic Solution of Stochastic Differential Equations

Abstract

In this paper, we make use of stochastic theta method to study the existence of the numerical approximation of random periodic solution. We prove that the error between the exact random periodic solution and the approximated one is at the $${1 \over 4}$$ order time step in mean sense when the initial time tends to ∞.