Y. Komori (2003), Multi-Colored Rooted Tree Analysis of the Order Conditions of Weak Schemes for Stochastic Differential Equations with a Multi-Dimensional Wiener Process, Technical Report CSSE-19, Faculty of Computer Science & Systems Engineering, Kyushu Institute of Technology.

Abstract
The aim of the present paper is to give the tractable way of seeking weak order conditions of a stochastic Runge-Kutta family for stochastic differential equations with a multi-dimensional Wiener process. This is accomplished by the extension of the rooted tree analysis for ordinary Runge-Kutta methods. It is illustrated that weak order conditions can be obtained directly from diagrams for multi-colored rooted trees in quite a transparent manner.

Note
The material in this report has been superseded by Y. Komori (2007).

The pdf file is obtainable from here.

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Last updated: 2007/03/07