随机微分方程Milstein方法的几乎必然及矩指数稳定性

J4 ›› 2011, Vol. 49 ›› Issue (06): 1058-1060.

随机微分方程Milstein方法的几乎必然及矩指数稳定性

张雨馨^1,2, 王鹏¹

1. 吉林大学数学学院, 长春 130012|2. 哈尔滨工程大学理学院, 哈尔滨 150001

收稿日期:2011-09-29 出版日期:2011-11-26 发布日期:2011-11-28
通讯作者: 王鹏 E-mail:pwang@jlu.edu.cn

Almost Sure and Moment Exponential Stability ofMilstein Methods for Stochastic Differential Equations

ZHANG Yuxin^1,2, WANG Peng¹

1. College of Mathematics, Jilin University, Changchun 130012, China;2. College of Science, Harbin Engineering University, Harbin 150001, China

Received:2011-09-29 Online:2011-11-26 Published:2011-11-28
Contact: WANG Peng E-mail:pwang@jlu.edu.cn

摘要/Abstract

摘要：

考虑随机微分方程Milstein方法的几乎必然及矩指数稳定性, 给出了当步长趋于零时极限意义下随机微分方程Milstein方法的稳定性, 并证明了在一定条件下显式和半隐式Milstein方法都具有这些稳定性.

关键词: Milstein方法, 半隐式Milstein方法, 线性增长条件

Abstract:

The almost sure and moment exponential stability of the Milstein scheme for stochastic differential equations were studied. We focused our attention on these stability properties in the limit as the timestep tends to zero and we proved that under proper conditions, explicit and semiimplicit Milstein methods maintain these stability properties.

Key words: Milstein method, semiimplicit Milstein method, linear growth condition

中图分类号:

O211.63

张雨馨, 王鹏. 随机微分方程Milstein方法的几乎必然及矩指数稳定性[J]. J4, 2011, 49(06): 1058-1060.

ZHANG Yu-Xin, WANG Feng. Almost Sure and Moment Exponential Stability ofMilstein Methods for Stochastic Differential Equations[J]. J4, 2011, 49(06): 1058-1060.

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