EXISTENCE AND MOMENT ESTIMATES FOR SOLUTIONS TO NEUTRAL STOCHASTIC FUNCTIONAL DIFFERENTIAL EQUATIONS

• 作者: Bing Li Daoyi Xu Lingying Teng Shujun Long Weisong Zhou
• 来源期刊: 微分方程年刊：英文版
• 学科: 数学
• 关键词: 中立型随机泛函微分方程 HILBERT空间 LIPSCHITZ系数 矩估计 指数稳定性 解的存在性 渐近行为 SONG
• 年，卷（期）: 2014,（1）
• 页码范围: 62-84
• 页数: 23页
• 分类号: O175.7

摘要

In this paper,we show the existence and uniqueness of solutions to a large class of SFDEs with the generalized local Lipschitzian coefficients.Some moment estimates of the solutions are given by establishing new It?o operator inequalities based on the Razumikhin technique.These estimates improve,extend and unify some related results including exponential stability of Mao(1997)[20],decay stability of Wu et al.(2010,2011)[32,33],Pavlovic et al.(2012)[24],asymptotic behavior of Luo et al.(2011)[18]and Song et al.(2013)[26].Moreover,stochastic version of Wintner theorem in continuous space is established by the comparison principle,which improve and extend the main results of Xu et al.(2008[39],2013[36]).When the methods presented are applied to the SFDEs with impulses and SFDEs in Hilbert spaces,we extend the related results of Govindana et al.(2013)[7],Liu et al.(2007)[15],Vinodkumar(2010)[29]and Xu et al.(2012)[35].Two examples are provided to illustrate the effectiveness of our results.