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

作     者：Daoyi Xu Bing Li Shujun Long Lingying Teng Weisong Zhou 

作者机构：Yangtze Center of Math.Sichuan University College of ScienceChongqing Jiaotong University College of Math.and Information ScienceLeshan Normal University College of Computer Science and Tech.Southwest University for Nationalities 

出 版 物：《Annals of Differential Equations》 (微分方程年刊（英文版）)

年 卷 期：2014年第30卷第1期

页      面：62-84页

学科分类：02[经济学] 0202[经济学-应用经济学] 020208[经济学-统计学] 07[理学] 0714[理学-统计学（可授理学、经济学学位）] 070103[理学-概率论与数理统计] 0701[理学-数学] 

基　　金：supported by National Natural Science Foundation of China under Grant 11271270 Fundamental Research Funds for the Central Universities under Grant 13NZYBS07 

主　　题：stochastic functional differential equations existence and uniqueness stochastic differential inequalities stability impulses equations in Hilbert spaces 

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 estima- tes of the solutions are given by establishing new Ito 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], Vinod- kumar （2010） [29] and Xu et al. （2012） [35]. Two examples are provided to illustrate the effectiveness of our results.