A General Implicit Splitting for Stabilizing Numerical Simulations of Langevin Equations

In this paper is described a general 2-nd order accurate (weak sense) procedure for stablizing Monte-Carlo simulations of Ito stochastic differential equations. The splitting procedure includes explicit Runge-Kutta methods, semi-implicit methods, and trapezoidal Rule. We prove the semi-implicit method of Oettinger and note that it may be generalized for arbitrary splittings.