求解刚性随机系统的分步向后Milstein方法

J4 ›› 2009, Vol. 47 ›› Issue (6): 1150-1154.

求解刚性随机系统的分步向后Milstein方法

王鹏¹, 韩月才²

1. 吉林大学数学研究所, 长春 130012； 2. 吉林大学数学学院, 长春 130012

收稿日期:2009-03-09 出版日期:2009-11-26 发布日期:2010-01-07
通讯作者: 王鹏 E-mail:pwang@jlu.edu.cn.

Splitstep Backward Milstein Methods for Stiff Stochastic Systems

WANG Peng¹, HAN Yuecai²

1. Institute of Mathematics, Jilin University, Changchun 130012, China;2. College of Mathematics, Jilin University, Changchun 130012, China

Received:2009-03-09 Online:2009-11-26 Published:2010-01-07
Contact: WANG Peng E-mail:pwang@jlu.edu.cn.

摘要/Abstract

摘要：

提出并分析了求解刚性It随机微分方程的分步向后Milstein方法, 基于分离技巧构造了DSSBM和MSSBM两种数值方法, 并证明了这两种方法都是一阶强收敛的. 通过讨论方法的数值稳定性和计算精度, 表明了所给方法在解决刚性随机系统时的优越性.

关键词: 随机微分方程； Milstein方法；均方稳定性

Abstract:

The authors presented and analyzed splitstep backward Milstein methods for solving It stochastic differential equations (SDEs). Two methods, a DSSBM method and an MSSBM method, were constructed based on the splitting technique. We proved that these methods are of strong order 1. The stability properties and numerical results show the effectiveness of these methods in the pathwise approximation of stiff SDEs.

Key words: stochastic differential equation, Milstein method, meansquare stability

中图分类号:

O241.8

王鹏, 韩月才. 求解刚性随机系统的分步向后Milstein方法[J]. J4, 2009, 47(6): 1150-1154.

WANG Peng, HAN Yuecai. Splitstep Backward Milstein Methods for Stiff Stochastic Systems[J]. J4, 2009, 47(6): 1150-1154.

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