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The material in this report has been superseded by Y. Komori (2007).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.
Last updated: 2007/03/07