Y. Komori, T. Mitsui and H. Sugiura (1997), Rooted tree analysis of the order conditions of ROW-type scheme for stochastic differential equations, BIT, 37 (1), 43-66.

Abstract
Numerical schemes for initial value problems of stochastic differential equations (SDEs) are considered so as to derive the order conditions of ROW-type schemes in the weak sense. Rooted tree analysis, the well-known useful technique for the counterpart of the ordinary differential equation case, is extended to be applicable to the SDE case. In our analysis, the roots are bi-colored corresponding to the ordinary and stochastic differential terms, whereas the vertices have four kinds of label corresponding to the terms derived from the ROW-schemes. The analysis brings a transparent way for the weak order conditions of the scheme. An example is given for illustration.

Note
The material in the paper has been superseded by Y. Komori (2007). Because the journal is in MathSciNet and Web of Science, additional information about the present paper is obtainable from the databases.

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