Composition of stochastic B-series with applications to implicit Taylor methods
Numerical Analysis
2011-01-26 v2
Abstract
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.
Keywords
Cite
@article{arxiv.1003.4397,
title = {Composition of stochastic B-series with applications to implicit Taylor methods},
author = {Kristian Debrabant and Anne Kværnø},
journal= {arXiv preprint arXiv:1003.4397},
year = {2011}
}
Comments
slight changes to improve readability. Changes resulting from the publishing process may not be reflected in the preprint version