无限时滞中立型随机泛函微分方程解的存在唯一性(英文)  

The Existence and Uniqueness of the Solutions for Neutral Stochastic Functional Differential Equations with Infinite Delay

作　　者：周少波[1] 薛明皋[2] 

机构地区：[1]华中科技大学数学系,湖北武汉430074 [2]华中科技大学管理学院,湖北武汉430074

出　　处：《应用数学》2008年第1期75-83,共9页Mathematica Applicata

基　　金：National Natural Science Foundation(70671047)

摘　　要：有限时滞随机泛函微分方程的存在唯一性已经得到较多的研究,但对于无限时滞随机泛函微分方程的性质极少.本文在不需要线性增长条件,在一致Lipschitz条件下证明了无限时滞中立型随机泛函微分方程的存在唯一性,给出了精确解和近似解的误差估计,最后给出了解的矩估计.The existence and uniqueness of stochastic functional differential equation with finite delay has been studied,but there is almost no work on the property of the neutral stochastic functional differential equations with infinite delay,The main aim of this paper is to close this gap. The paper establishes the existence and uniqueness theorem of solutions to the neutral stochastic functional dif- ferential equations with infinite delay（short for INSFDEs） under the uniform Lipschitz condition （the linear growth condition is weaked）, and gives the estimate for the error between approximate solution and accurate solution. Finally,the moment estimate for the solution is obtained.

关 键 词：存在性 唯一性 中立型随机泛函微分方程 无限时滞 

分 类 号：TP13[自动化与计算机技术—控制理论与控制工程]