Stochastic Runge-Kutta methods for Itô sodes with small noise

Evelyn Buckwar*, Andreas Rößler, Renate Winkler

*Corresponding author for this work
10 Citations (Scopus)


We consider stochastic Runge-Kutta methods for Itô stochastic ordinary differential equations, and study their mean-square convergence properties for problems with small multiplicative noise or additive noise. First we present schemes where the drift part is approximated by well-known methods for deterministic ordinary differential equations, and a Maruyama term is used to discretize the diffusion. Further, we suggest improving the discretization of the diffusion part by taking into account also mixed classical-stochastic integrals, and we present a suitable class of fully derivativefree methods. We show that the relation of the applied step-sizes to the smallness of the noise is essential to decide whether the new methods are worth the effort. Simulation results illustrate the theoretical findings.

Original languageEnglish
JournalSIAM Journal on Scientific Computing
Issue number4
Pages (from-to)1789-1808
Number of pages20
Publication statusPublished - 23.08.2010


Dive into the research topics of 'Stochastic Runge-Kutta methods for Itô sodes with small noise'. Together they form a unique fingerprint.

Cite this