Pathwise Estimation of Stochastic Differential Equations with Unbounded Delay and Its Application to Stochastic Pantograph Equations

被引：13
|
作者：
Meng, Xuejing [1 ]
Hu, Shigeng [1 ]
Wu, Ping [2 ]
机构：
[1] Huazhong Univ Sci & Technol, Sch Math & Stat, Wuhan 430074, Peoples R China
[2] AF Radar Acad, Dept Basics, Wuhan 430019, Peoples R China
来源：
ACTA APPLICANDAE MATHEMATICAE | 2011年 / 113卷 / 02期
关键词：
Stochastic differential equation; Unbounded delay; Pathwise estimation; Pantograph equation; NEURAL-NETWORKS; STABILITY; CONVERGENCE; UNIQUENESS; EXISTENCE;
D O I：
10.1007/s10440-010-9596-0
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The existence and uniqueness of the global solution of stochastic differential equations with discrete variable delay is investigated in this paper, and the pathwise estimation is also done by using Lyapunov function method and exponential martingale inequality. The results can be used not only in the case of bounded delay but also in the case of unbounded delay. As the applications, this paper considers the pathwise estimation of solutions of stochastic pantograph equations.
引用
收藏
页码：231 / 246
页数：16
相关论文
共 50 条
  • [1] Pathwise Estimation of Stochastic Differential Equations with Unbounded Delay and Its Application to Stochastic Pantograph Equations
    Xuejing Meng
    Shigeng Hu
    Ping Wu
    [J]. Acta Applicandae Mathematicae, 2011, 113 : 231 - 246
  • [2] General decay pathwise stability of neutral stochastic differential equations with unbounded delay
    Yang Zi Hu
    Fu Ke Wu
    Cheng Ming Huang
    [J]. Acta Mathematica Sinica, English Series, 2011, 27 : 2153 - 2168
  • [3] AN EULER SCHEME FOR STOCHASTIC DELAY DIFFERENTIAL EQUATIONS ON UNBOUNDED DOMAINS: PATHWISE CONVERGENCE
    Akhtari, Bahareh
    Babolian, Esmail
    Neuenkirch, Andreas
    [J]. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2015, 20 (01): : 23 - 38
  • [4] General Decay Pathwise Stability of Neutral Stochastic Differential Equations with Unbounded Delay
    Hu, Yang Zi
    Wu, Fu Ke
    Huang, Cheng Ming
    [J]. ACTA MATHEMATICA SINICA-ENGLISH SERIES, 2011, 27 (11) : 2153 - 2168
  • [5] STABILITY OF STOCHASTIC DIFFERENTIAL EQUATIONS WITH UNBOUNDED DELAY
    Zhencheng Fan (Dept. of Math.
    ) Yu Xiao (Dept. of Math.
    [J]. Annals of Applied Mathematics, 2009, 25 (03) : 309 - 315
  • [6] On delay estimation for stochastic differential equations
    Kutoyants, YA
    [J]. STOCHASTICS AND DYNAMICS, 2005, 5 (02) : 333 - 342
  • [7] On the pathwise approximation of stochastic differential equations
    Tony Shardlow
    Phillip Taylor
    [J]. BIT Numerical Mathematics, 2016, 56 : 1101 - 1129
  • [8] On the pathwise approximation of stochastic differential equations
    Shardlow, Tony
    Taylor, Phillip
    [J]. BIT NUMERICAL MATHEMATICS, 2016, 56 (03) : 1101 - 1129
  • [9] ON STOCHASTIC FUNCTIONAL-DIFFERENTIAL EQUATIONS WITH UNBOUNDED DELAY
    TUDOR, C
    [J]. SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 1987, 18 (06) : 1716 - 1725
  • [10] Pathwise stochastic control and a class of stochastic partial differential equations
    Bhauryal, Neeraj
    Cruzeiro, Ana Bela
    Oliveira, Carlos
    [J]. arXiv, 2023,
12345