A CLASS OF STOCHASTIC FUNCTIONAL DIFFERENTIAL EQUATIONS WITH MARKOVIAN SWITCHING

被引：1
|
作者：
Hu, Yangzi [1 ]
Wu, Fuke [1 ]
机构：
[1] Huazhong Univ Sci & Technol, Sch Math & Stat, Wuhan 430074, Hubei, Peoples R China
来源：
JOURNAL OF INTEGRAL EQUATIONS AND APPLICATIONS | 2011年 / 23卷 / 02期
基金：
中国国家自然科学基金;
关键词：
Ito formula; Markovian chain; global solution; stochastically ultimate boundedness; moment average boundedness in time; LASALLE-TYPE THEOREMS; DELAY EQUATIONS; STABILITY;
D O I：
10.1216/JIE-2011-23-2-223
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
This paper investigates a class of stochastic functional differential equations with Markovian switching. Under the local Lipschitz condition but not the linear growth condition, this paper establishes existence-and-uniqueness theorems for the global solutions of these equations. This paper also examines asymptotic boundedness of the global solution, including boundedness in moment, stochastically ultimate boundedness and the moment average boundedness in time. To illustrate our idea more clearly, we consider a scalar stochastic polynomial equation and a special n-dimensional equation in detail.
引用
收藏
页码：223 / 252
页数：30
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