Classification of stochastic Runge-Kutta methods for the weak approximation of stochastic differential equations

被引:28
作者
Debrabant, Kristian [1 ]
Roessler, Andreas [1 ]
机构
[1] Tech Univ Darmstadt, Fachbereich Math, D-64289 Darmstadt, Germany
关键词
stochastic Runge-Kutta method; stochastic differential equation; classification; weak approximation; optimal scheme;
D O I
10.1016/j.matcom.2007.04.016
中图分类号
TP39 [计算机的应用];
学科分类号
081203 ; 0835 ;
摘要
In the present paper, a class of stochastic Runge-Kutta methods containing the second order stochastic Runge-Kutta scheme due to E. Platen for the weak approximation of W stochastic differential equation systems with a multi-dimensional Wiener process is considered. Order 1 and order 2 conditions for the coefficients of explicit stochastic Runge-Kutta methods are solved and the solution space of the possible coefficients is analyzed. A full classification of the coefficients for such stochastic Runge-Kutta schemes of order 1 and two with minimal stage numbers is calculated. Further, within the considered class of stochastic Runge-Kutta schemes coefficients for optimal schemes in the sense that additionally some higher order conditions are fulfilled are presented. (c) 2007 IMACS. Published by Elsevier B.V. All rights reserved.
引用
收藏
页码:408 / 420
页数:13
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