Stepanov-Like Pseudo Almost Automorphic Solutions to Some Stochastic Differential Equations

被引：0
作者：
Yong-Kui Chang
Zhuan-Xia Cheng
G. M. N’Guérékata
机构：
[1] Xidian University,School of Mathematics and Statistics
[2] Lanzhou Jiaotong University,Department of Mathematics
[3] Morgan State University,Department of Mathematics
来源：
Bulletin of the Malaysian Mathematical Sciences Society | 2016年 / 39卷
关键词：
Stepanov-like pseudo almost automorphic stochastic processes; Square-mean pseudo almost automorphy; Stochastic differential equations; 34K14; 60H10; 35B15; 34F05;
D O I：
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中图分类号：
学科分类号：
摘要：
In this paper, we introduce a new concept of S2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$S^{2}$$\end{document}-pseudo almost automorphy for stochastic processes. We apply the results obtained to investigate the existence and uniqueness of S2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$S^{2}$$\end{document}-pseudo almost automorphic mild solutions to some stochastic differential equations in a real separable Hilbert space. Our main results extend some known ones in the sense of square-mean pseudo almost automorphy or S2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$S^{2}$$\end{document}-almost automorphy for stochastic processes.
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页码：181 / 197
页数：16
相关论文
共 43 条
[1]  
Bezandry P(2008)Existence of Electron. J. Qual. Theory Differ. Equ. 35 1-19
[2]  
Diagana T(2011)-almost periodic solutions to a class of nonautonomous stochastic evolution equations Afr. Diaspora J. Math. 12 60-79
[3]  
Bezandry P(1962)-th mean pseudo almost automorphic mild solutions to some nonautonomous stochastic differential equations Proc. Natl Acad. Sci. USA 48 2039-2043
[4]  
Diagana T(1964)A new approach to almost automorphicity Proc. Natl Acad. Sci. USA 52 907-910
[5]  
Bochner S(2011)Continuous mappings of almost automorphic and almost periodic functions Stochastics 83 259-275
[6]  
Bochner S(2011)Existence and exponential stability of almost automorphic mild solutions for stochastic functional differential equations Nonlinear Anal. RWA 12 1130-1139
[7]  
Cao JF(2011)Stepanov-like almost automorphy for stochastic processes and applications to stochastic differential equations J. Funct. Anal. 261 69-89
[8]  
Yang QG(2009)Square-mean pseudo almost automorphic process and its application to stochastic evolution equations Nonlinear Anal. 70 3781-3790
[9]  
Huang ZT(2010)Existence of pseudo-almost automorphic solutions to some abstract differential equations with Proc. Am. Math. Soc. 138 3689-3701
[10]  
Chang YK(1982)-pseudo-almost automorphic coefficients J. Math. Anal. Appl. 90 12-44
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