General Decay Pathwise Stability of Neutral Stochastic Differential Equations with Unbounded Delay

Without the linear growth condition, by the use of Lyapunov function, this paper estab- lishes the existence~and-uniqueness theorem of global solutions to a class of neutral stochastic differen- tim equations with unbounded delay, and examines the pathwise stability of this solution with general dec...

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Bibliographic Details
Published inActa mathematica Sinica. English series Vol. 27; no. 11; pp. 2153 - 2168
Main Authors Hu, Yang Zi, Wu, Fu Ke, Huang, Cheng Ming
Format Journal Article
LanguageEnglish
Published Heidelberg Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society 01.11.2011
Springer Nature B.V
Subjects
Brownian motion
Decay
Decay rate
Delay
Differential equations
Lyapunov functions
Lyapunov函数
Mathematical analysis
Mathematics
Mathematics and Statistics
Stability
Stochastic models
Stochasticity
Studies
中立型
唯一性定理
无界时滞
无限延迟
稳定性
衰变率
随机微分方程
Pathwise stability
34K40
60H10
34K50
unbounded delay
general decay rate
matrix
neutral stochastic differential equations
34K20
Online AccessGet full text
ISSN1439-8516
1439-7617
DOI10.1007/s10114-011-9456-5

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Summary:Without the linear growth condition, by the use of Lyapunov function, this paper estab- lishes the existence~and-uniqueness theorem of global solutions to a class of neutral stochastic differen- tim equations with unbounded delay, and examines the pathwise stability of this solution with general decay rate. As an application of our results, this paper also considers in detail a two-dimensional unbounded delay neutral stochastic differential equation with polynomial coefficients.
Bibliography:Pathwise stability, neutral stochastic differential equations, unbounded delay, M-matrix, general decay rate
11-2039/O1
Without the linear growth condition, by the use of Lyapunov function, this paper estab- lishes the existence~and-uniqueness theorem of global solutions to a class of neutral stochastic differen- tim equations with unbounded delay, and examines the pathwise stability of this solution with general decay rate. As an application of our results, this paper also considers in detail a two-dimensional unbounded delay neutral stochastic differential equation with polynomial coefficients.
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ISSN:1439-8516
1439-7617
DOI:10.1007/s10114-011-9456-5