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

被引：8

作者：

Debrabant, Kristian ^{[1
]}

Kvaerno, Anne ^{[2
]}

机构：

[1] Tech Univ Darmstadt, Fachbereich Math, D-64293 Darmstadt, Germany

[2] Norwegian Univ Sci & Technol, Dept Math Sci, N-7491 Trondheim, Norway

来源：

APPLIED NUMERICAL MATHEMATICS | 2011年 / 61卷 / 04期

关键词：

Stochastic Taylor method; Stochastic differential equation; Order conditions; Weak approximation; Strong approximation; Stochastic B-series; RUNGE-KUTTA METHODS; ROOTED TREE ANALYSIS; DIFFERENTIAL-EQUATIONS; ORDER CONDITIONS; EXPANSIONS; SCHEME;

D O I：

10.1016/j.apnum.2010.11.014

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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 Ito SDEs. (C) 2010 IMACS. Published by Elsevier B.V. All rights reserved.

引用

页码：501 / 511

页数：11

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