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一类随机泛函微分方程带随机步长的EM逼近的渐近稳定

马丽 马瑞楠

马丽, 马瑞楠. 一类随机泛函微分方程带随机步长的EM逼近的渐近稳定[J]. 应用数学和力学, 2019, 40(1): 97-107. doi: 10.21656/1000-0887.390057
引用本文: 马丽, 马瑞楠. 一类随机泛函微分方程带随机步长的EM逼近的渐近稳定[J]. 应用数学和力学, 2019, 40(1): 97-107. doi: 10.21656/1000-0887.390057
MA Li, MA Ruinan. Almost Sure Asymptotic Stability of the Euler-Maruyama Method With Random Variable Stepsizes for Stochastic Functional Differential Equations[J]. Applied Mathematics and Mechanics, 2019, 40(1): 97-107. doi: 10.21656/1000-0887.390057
Citation: MA Li, MA Ruinan. Almost Sure Asymptotic Stability of the Euler-Maruyama Method With Random Variable Stepsizes for Stochastic Functional Differential Equations[J]. Applied Mathematics and Mechanics, 2019, 40(1): 97-107. doi: 10.21656/1000-0887.390057

一类随机泛函微分方程带随机步长的EM逼近的渐近稳定

doi: 10.21656/1000-0887.390057
基金项目: 国家自然科学基金(11861029);海南省高等学校科学研究项目(重点项目)(Hnky2018ZD6);海南省自然科学基金(面上项目)(118MS040);海南省自然科学基金(创新研究团队项目)(2018CXTD338)
详细信息
    作者简介:

    马丽(1979—),女,副教授,博士,硕士生导师(通讯作者. E-mail: malihnsd@163.com).

  • 中图分类号: O211.62

Almost Sure Asymptotic Stability of the Euler-Maruyama Method With Random Variable Stepsizes for Stochastic Functional Differential Equations

Funds: The National Natural Science Foundation of China(11861029)
  • 摘要: 研究了一类带有限延迟的随机泛函微分方程的Euler-Maruyama(EM)逼近,给出了该方程的带随机步长的EM算法,得到了随机步长的两个特点:首先,有限个步长求和是停时;其次,可列无限多个步长求和是发散的.最终,由离散形式的非负半鞅收敛定理,得到了在系数满足局部Lipschitz条件和单调条件下,带随机步长的EM数值解几乎处处收敛到0.该文拓展了2017年毛学荣关于无延迟的随机微分方程带随机步长EM数值解的结果.
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出版历程
  • 收稿日期:  2018-02-06
  • 修回日期:  2018-08-22
  • 刊出日期:  2019-01-01

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