A semi-analytic explicit integrator for stochastic differential equations driven by multidimensional linear multiplicative noise

Abstract

Many important stochastic differential equations (SDE) used for modeling noisy dynamical systems are driven by multidimensional linear multiplicative noise. In this work we introduce an explicit, stable and easily implementable numerical integrator specially devised for such a class of stochastic systems. The pathwise convergence -under non-standard assumption on the coefficients of the SDE- is studied. Remarkably, we show that even though the proposed method is explicit, it is unconditionally MS-stable and consequently much more efficient than methods commonly used in the literature to stably integrate this kind of equations. Some questions related to the computational implementation of the method are also discussed.