A General Implicit Splitting for Stabilizing Numerical Simulations of Itô Stochastic Differential Equations

In this paper we describe a general 2nd-order accurate (weak sense) procedure for stabilizing Monte-Carlo simulations of Itô stochastic differential equations. The splitting procedure includes explicit Runge--Kutta (Heun) methods, semi-implicit methods, and the trapezoidal rule. We prove the semi-implicit method of Öttinger [Stochastic Processes in Polymeric Fluids, Springer-Verlag, Berlin, 1996] for stabilizing simulations in the presence of nonlinear drift coefficients.