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中立型随机延迟微分方程θ-方法的均方稳定性 被引量：1

Mean-Square Stability of θ-Methods for Neutral Nonlinear Stochastic Delay Differential Equations
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摘要 讨论θ-方法用于求解非线性中立型随机延迟微分方程初值问题时数值解的稳定性,给出了θ-方法均方稳定的一个充分条件. The mean-square stability of Euler method is investigated for nonlinear neutral stochastic delay differential equations. It is proved that the numerical method is mean-square stable（MS-stable） under a sufficient condition.
作者 王文强
机构地区 湘潭大学数学与计算科学学院
出处 《吉首大学学报（自然科学版）》 CAS 2014年第2期10-14,共5页 Journal of Jishou University(Natural Sciences Edition)
基金 国家自然科学基金资助项目(11271311 11171352)
关键词 中立型随机延迟微分方程 Θ-方法 均方稳定 neutral stochastic delay differential equations θ-methods mean-square stable
分类号 O175.13 [理学—基础数学]
  • 相关文献

参考文献15

  • 1HU Yaozhong,SALAH-ELDIN A MOHAMMED,YAN Feng.Discrete-Time Approximations of Stochastic Delay Equa tions:The Milstein Scheme[J].The Annals of Probability,2004,32(1A):265-314.
  • 2CAO Wanrong,LIU Mingzhu,FAN Zhencheng.MS-Stability of the Euler-Maruyama Method for Stochastic Differential Delay Equations[J].Applied Mathematics and Computation,2004,159:127-135.
  • 3CAO Wanrong.The Convergence and Stability of Some Numerical Methods for Stochastic Differential Delay Equation[D].Harbin:Harbin Institute of Technology,2004.
  • 4CHRISTOPHER T H BAKER,EVELYN BUCKWAR.Exponential Stability in p-th Mean of Solutions,and of Convergent Euler-Type Solutions,of Stochastic Delay Differential Equations[J].Journal of Computational and Applied Mathematics,2005,184:404-427.
  • 5WANG Zhiyong,ZHANG Chengjian.An Analysis of Stability of Milstein Method for Stochastic Differential Equations with Delay[J].Computers and Mathematics with Applications,2006,51:1 445-1 452.
  • 6NORBERT HOFMANN,THOMAS M(U)LLER-GRONBACH.A Modified Milstein Scheme for Approximation of Stochastic Delay Differential Equations with Constant Time Lag[J].Journal of Computational and Applied Mathematics,2006,197:89-121.
  • 7王文强,黄山,李寿佛.非线性随机延迟微分方程Euler-Maruyama方法的均方稳定性[J].计算数学,2007,29(2):217-224. 被引量：10
  • 8WANG Wenqiang,LI Shoufu,HUANG Shan.Convergence of Semi-Implicit Euler Methods for Nonlinear Stochastic Delay Differential Equations[J].Journal of Yunnan University:Natural Sciences Edition,2008,30(1):11-15.
  • 9WANG Wenqiang.Convergence and Stability of Several Numerical Methods for Nonlinear Stochastic Delay Differential Equations[D].Xiangtan:Xiangtan University,2007.
  • 10LUO Jiaowan.A Note on Exponential Stability in p-th Mean of Solutions of Stochastic Delay Differential Equations[J].Journal of Computational and Applied Mathematics,2007,198 (1):143-148.

二级参考文献8

  • 1曹婉容,刘明珠.随机延迟微分方程Euler-Maruyama数值方法的T-稳定性[J].哈尔滨工业大学学报,2005,37(3):303-305. 被引量：10
  • 2曹婉容,刘明珠.随机延迟微分方程半隐式Milstein数值方法的稳定性[J].哈尔滨工业大学学报,2005,37(4):446-448. 被引量：8
  • 3Cao Wanrong,Liu Mingzhu and Fan Zhencheng,MS-stability of the Euler-Maruyama method for stochastic differential delay equations.Applied Mathematics and Computation,2004,159:127-135.
  • 4Liu Mingzhu,Cao Wanrong and Fan Zhencheng,Convergence and stability of the semiimplicit Euler method for a linear stochastic differential delay equation.J.Comput.Appl.Math.,2004,170(2):255-268.
  • 5Christopher T.H.Baker,Evelyn Buckwar.Exponential stability in p-th mean of solutions,and of convergent Euler-type solutions,of stochastic delay differential equations.Journal of Computational and Applied Mathematics,2005,184:404-427.
  • 6Wang Zhiyong,Zhang Chengjian,An analysis of stability of Milstein method for stochastic differential equations with delay.Computers and Mathematics with Applications,2006,51:1445-1452.
  • 7Mao X.Razumikhin-Type theoremson exponential stability of stochastic functional differential equations.Stochastic Processes and their Applications,1996,65:233-250.
  • 8Mao Xuerong.Stochastic differential equations and applications.Horwood,New York,1997.

共引文献9

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二级引证文献4

吉首大学学报（自然科学版）
2014年 第2期

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