Computer simulations of multiplicative stochastic differential equations

Abstract

A class of robust algorithms for the computer simulation of stochastic differential equations with multiplicative noise is investigated. Excellent agreement is obtained with the known analytic behaviour of the Kubo oscillator in the white noise limit. The algorithms include a known first-order one-dimensional explicit method, as well as implicit methods of increased stability. A distinction is drawn between classes of stochastic differential equations depending on the type of spatial variation or curvature defined by the diffusion tensor. This allows greatly simplified numerical implementations of the new algorithms in certain cases. The results of different techniques are compared for the case of the Kubo oscillator, where a semi-implicit technique gives the greatest accuracy.