Numerical Integration of Multiplicative-Noise Stochastic Differential Equations

A two-stage, Runge–Kutta algorithm for vector Itô (and, by transform, also Stratonovich) stochastic differential equations with multiplicative noise has been developed. The method is second order accurate; but, for vanishing drift the algorithm yields a martingale independent of step size. Several examples are included to illustrate our method. A discussion of errors shows that sample size can be as important as truncation.