@techreport{oai:kyutech.repo.nii.ac.jp:00000677, author = {Komori, Yoshio and 小守, 良雄}, month = {Oct}, note = {The aim of the present paper is to give the tractable way of seeking weak orderconditions of a stochastic Runge-Kutta family for stochastic differential equationswith a multi-dimensional Wiener process. This is accomplished by the extensionof the rooted tree analysis for ordinary Runge-Kutta methods. It is illustratedthat weak order conditions can be obtained directly from diagrams for multi-coloredrooted trees in quite a transparent manner., [Remark] The material in this report has been superseded by the following paper: Y. Komori (2007), Multi-colored rooted tree analysis of the weak order conditions of a stochastic Runge-Kutta family, Applied Numerical Mathematics, 57(2), 147-165.}, title = {Multi-Colored Rooted Tree Analysis of the Order Conditions of Weak Schemes for Stochastic Differential Equations with a Multi-Dimensional Wiener Process}, year = {2003}, yomi = {コモリ, ヨシオ} }