A randomized Milstein method for stochastic differential equations with non-differentiable drift coefficients by Kruse, R, Wu, Y

“…In this paper a drift-randomized Milstein method is introduced for the numerical solution of non-autonomous stochastic differential equations with non-differentiable drift coefficient functions. …”

Truncated Euler-Maruyama method for classical and time-changed non-autonomous stochastic differential equations by Liu, W, Mao, X, Tang, J, Wu, Y

“…The truncated Euler-Maruyama (EM) method is proposed to approximate a class of non-autonomous stochastic differential equations (SDEs) with the Hölder continuity in the temporal variable and the super-linear growth in the state variable. …”

The random periodic solution of a stochastic differential equation with a monotone drift and its numerical approximation by Wu, Y

“…In this paper we study the existence and uniqueness of the random periodic solution for a stochastic differential equation with a one-sided Lipschitz condition (also known as monotonicity condition) and the convergence of its numerical approximation via the backward Euler-Maruyama method. …”

Backward Euler–Maruyama method for the random periodic solution of a stochastic differential equation with a monotone drift by Wu, Y

“…In this paper, we study the existence and uniqueness of the random periodic solution for a stochastic differential equation with a one-sided Lipschitz condition (also known as monotonicity condition) and the convergence of its numerical approximation via the backward Euler–Maruyama method. …”

Anticipating random periodic solutions I: SDEs with multiplicative linear noise by Feng, C, Wu, Y, Zhao, H

“…In this paper, we study the existence of random periodic solutions for semilinear stochastic differential equations. We identify them as solutions of coupled forward–backward infinite horizon stochastic integral equations (IHSIEs), using the “substitution theorem” of stochastic differential equations with anticipating initial conditions. …”