Continuous weak approximation for stochastic differential equations

Authors:
Kristian Debrabant;Andreas Röíler
Affiliations:
Technische Universität Darmstadt, Fachbereich Mathematik, Schlossgartenstr. 7, D-64289 Darmstadt, Germany;Technische Universität Darmstadt, Fachbereich Mathematik, Schlossgartenstr. 7, D-64289 Darmstadt, Germany
Venue:
Journal of Computational and Applied Mathematics
Year:
2008

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Abstract

A convergence theorem for the continuous weak approximation of the solution of stochastic differential equations (SDEs) by general one-step methods is proved, which is an extension of a theorem due to Milstein. As an application, uniform second order conditions for a class of continuous stochastic Runge-Kutta methods containing the continuous extension of the second order stochastic Runge-Kutta scheme due to Platen are derived. Further, some coefficients for optimal continuous schemes applicable to Ito SDEs with respect to a multi-dimensional Wiener process are presented.