Stepanov-like almost automorphy for stochastic processes and applications to stochastic differential equations

被引：37
|
作者：
Chang, Yong-Kui [1 ,2 ]
Zhao, Zhi-Han [1 ]
N'Guerekata, G. M. [3 ]
Ma, Ruyun [2 ]
机构：
[1] Lanzhou Jiaotong Univ, Dept Math, Lanzhou 730070, Gansu, Peoples R China
[2] NW Normal Univ, Dept Math, Lanzhou 730070, Peoples R China
[3] Morgan State Univ, Dept Math, Baltimore, MD 21251 USA
来源：
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS | 2011年 / 12卷 / 02期
基金：
中国博士后科学基金;
关键词：
Stepanov-like almost automorphy; Square-mean almost automorphy; Stochastic differential equations; ALMOST-PERIODIC SOLUTIONS; MILD SOLUTIONS; EXISTENCE;
D O I：
10.1016/j.nonrwa.2010.09.007
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we introduce a new concept of Stepanov-like almost automorphy (or S-2-almost automorphy) for stochastic processes. We use the results obtained to investigate the existence and uniqueness of a Stepanov-like almost automorphic mild solution to a class of nonlinear stochastic differential equations in a real separable Hilbert space. Our main results extend some known ones in the sense of square-mean almost automorphy. (C) 2010 Elsevier Ltd. All rights reserved.
引用
收藏
页码：1130 / 1139
页数：10
相关论文
共 50 条
  • [21] Metrical Stepanov Almost Automorphy and Applications
    Belkacem Chaouchi
    Marko Kostić
    Halis Can Koyuncuoğlu
    [J]. Bulletin of the Iranian Mathematical Society, 2024, 50
  • [22] Almost automorphy and various extensions for stochastic processes
    Bedouhene, Fazia
    Challali, Nouredine
    Mellah, Omar
    de Fitte, Paul Raynaud
    Smaali, Mannal
    [J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2015, 429 (02) : 1113 - 1152
  • [23] Stepanov-like doubly weighted pseudo almost automorphic processes and its application to Sobolev-type stochastic differential equations driven by G-Brownian motion
    Yang, Qigui
    Zhu, Ping
    [J]. MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2017, 40 (18) : 6602 - 6622
  • [24] Stepanov-Like Pseudo-Almost Periodicity and Semilinear Differential Equations with Uniform Continuity
    Hong-Xu Li
    Li-Li Zhang
    [J]. Results in Mathematics, 2011, 59 : 43 - 61
  • [25] STEPANOV-LIKE ALMOST AUTOMORPHIC SOLUTIONS FOR NONAUTONOMOUS EVOLUTION EQUATIONS
    Fatajou, Samir
    Nguyen Van Minh
    N'Guerekata, Gaston M.
    Pankov, Alexander
    [J]. ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2007,
  • [26] Stepanov-Like Pseudo-Almost Periodicity and Semilinear Differential Equations with Uniform Continuity
    Li, Hong-Xu
    Zhang, Li-Li
    [J]. RESULTS IN MATHEMATICS, 2011, 59 (1-2) : 43 - 61
  • [27] Doubly-weighted pseudo almost automorphic solutions for stochastic dynamic equations with Stepanov-like coefficients on time scales
    Dhama, Soniya
    Abbas, Syed
    Debbouche, Amar
    [J]. Chaos, Solitons and Fractals, 2020, 137
  • [28] Stepanov-like almost automorphic functions and monotone evolution equations
    N'Guerekata, Gaston M.
    Pankov, Alexander
    [J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2008, 68 (09) : 2658 - 2667
  • [29] Some properties of Stepanov-like almost automorphic functions and applications to abstract evolution equations
    Ding, Hui-Sheng
    Liang, Jin
    Xiao, Ti-Jun
    [J]. APPLICABLE ANALYSIS, 2009, 88 (07) : 1079 - 1091
  • [30] Composition of Stepanov-like pseudo almost automorphic functions and applications to nonautonomous evolution equations
    Fan, Zhenbin
    Liang, Jin
    Xiao, Ti-Jun
    [J]. NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2012, 13 (01) : 131 - 140
12345