广西师范大学学报（自然科学版） ›› 2012, Vol. 30 ›› Issue (2): 35-41.

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随机微分方程1.5阶随机Taylor方法的指数稳定性

张浩奇1, 张浩敏1,2   

  1. 1.桂林理工大学理学院,广西桂林541004;
    2.广西空间信息与测绘重点实验室,广西桂林541004
  • 收稿日期:2012-03-08 出版日期:2012-06-20 发布日期:2018-12-03
  • 通讯作者: 张浩敏(1978—),男,湖南武冈人,桂林理工大学副教授。E-mail:zhanghm@glite.edu.cn
  • 基金资助:
    国家自然科学基金资助项目(11101101);广西自然科学基金资助项目(20011GXNSFD018003);广西空间信息与测绘重点实验室资助课题(桂科能1103108-08)

Exponential Stability of 1.5 Order Stochastic Taylor Method for Stochastic Differential Equations

ZHANG Hao-qi1, ZHANG Hao-min1,2   

  1. 1.College of Science,Guilin University of Technology,Guilin Guangxi 541004,China;
    2.Guangxi Key Laboratory of Spatial Information and Geomatics,Guilin Guangxi 541004,China
  • Received:2012-03-08 Online:2012-06-20 Published:2018-12-03

摘要： 本文针对线性随机微分方程,首先证明了强1.5阶隐式随机Taylor方法能无条件保持解析解几乎处处指数稳定性;其次证明了当0＜p＜2时,该数值算法能无条件保持解析解的p阶矩指数稳定性(即小阶矩指数稳定性),并给出了验证所得结论的数值算例。

关键词: 线性随机微分方程, 强1.5阶隐式随机Taylor方法, 几乎处处指数稳定, 矩指数稳定

Abstract: In this paper,of implicit stochastic Taylor method with the exponential stability of 1.5 order and feather of almost sure and small-moments is investigated.It is proved that the numerical method can unconditionally inherit the almost sure exponential stability andthe p-th moment exponential stability of the underlying system when 0＜p＜2.An illustrative numerical example is presented to demonstrate the theoretical results.

Key words: linear stochastic differential equation, strong 1.5 order implicit stochastic Taylor method, almost sure exponential stability, momentexponential stability

中图分类号: 

  • O211.63
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