Rooted tree analysis of the order conditions of row-type scheme for stochastic differential equations |
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Authors: | Yoshio Komori Taketomo Mitsui Hiroshi Sugiura |
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Institution: | (1) Department of Information Engineering, School of Engineering Nagoya University, 464-01 Nagoya, Japan;(2) Graduate School of Human Informatics, Nagoya University, 464-01 Nagoya, Japan |
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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. |
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Keywords: | 65U05 60H10 65L06 65L05 |
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