Composition of stochastic B-series with applications to implicit Taylor methods

Details Composition of stochastic B-series with applications to implicit Taylor methods Composition of stochastic B-series with applications to implicit Taylor methods

2010-03-23

arxiv.org/abs/1003.4397v2

Applied Numerical Mathematics 61, No. 4, (2011), pp. 501-511

Mathematics

Numerical Analysis

slight changes to improve readability. Changes resulting from the publishing process may not be reflected in the preprint vers

Scientific paper

10.1016/j.apnum.2010.11.014

In this article, we construct a representation formula for stochastic
B-series evaluated in a B-series. This formula is used to give for the first
time the order conditions of implicit Taylor methods in terms of rooted trees.
Finally, as an example we apply these order conditions to derive in a simple
manner a family of strong order 1.5 Taylor methods applicable to It\^o SDEs.

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