An explicit numerical method for random differential equations driven by diffusion-type noises

Abstract

In this work we propose a numerical integrator with appealing B-stability properties for the effective integration of Random Ordinary Differential Equations (RDEs) under the influence of Itˆo-diffusion noise. Basically the introduced integrators are obtained by transforming the RDE to a stochastic differential equation and then adapting the well-known local linearization approach to the special structure of the resulting equation. The introduced method enables to overcome much of the numerical instability that are frequently found when using explicit integrators and is computationally more efficient than stable implicit ones. Results on the convergence and stability of the proposed method are discussed and we also outline some key issues concerning the efficient computational implementation of the corresponding numerical schemes.