Rooted tree analysis for order conditions of stochastic Runge-Kutta methods for the weak approximation of stochastic differential equations

Andreas Rößler*

*Corresponding author for this work
46 Citations (Scopus)

Abstract

A general class of stochastic Runge-Kutta methods for the weak approximation of Itô and Stratonovich stochastic differential equations with a multi-dimensional Wiener process is introduced. Colored rooted trees are used to derive an expansion of the solution process and of the approximation process calculated with the stochastic Runge-Kutta method. A theorem on general order conditions for the coefficients and the random variables of the stochastic Runge-Kutta method is proved by rooted tree analysis. This theorem can be applied for the derivation of stochastic Runge-Kutta methods converging with an arbitrarily high order.

Original languageEnglish
JournalStochastic Analysis and Applications
Volume24
Issue number1
Pages (from-to)97-134
Number of pages38
ISSN0736-2994
DOIs
Publication statusPublished - 01.03.2006

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