Square-mean Almost Periodic Solutions to Some Stochastic Evolution Equations

This paper concerns the square-mean almost periodic mild solutions to a class of abstract nonautonomous functional integro-differential stochastic evolution equations in a real separable Hilbert space. By using the so-called ＂Acquistapace–Terreni＂ conditions and the Banach fixed point theorem, we es...

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Bibliographic Details
Published in:Acta mathematica Sinica. English series 2014-05, Vol.30 (5), p.881-898
Main Author: Li, Xi Liang
Format: Article
Language:English
Subjects:
Asymptotic properties
Banach spaces
Banach不动点定理
Brownian motion
Differential equations
Evolution
Existence theorems
Hilbert space
Mathematical analysis
Mathematical models
Mathematics
Mathematics and Statistics
Random variables
Stability
Stochastic models
Stochasticity
Studies
Theorems
Uniqueness
可分Hilbert空间
平均
概周期解
渐近稳定性
积分微分方程
随机发展方程
随机微分方程
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Summary:This paper concerns the square-mean almost periodic mild solutions to a class of abstract nonautonomous functional integro-differential stochastic evolution equations in a real separable Hilbert space. By using the so-called ＂Acquistapace–Terreni＂ conditions and the Banach fixed point theorem, we establish the existence, uniqueness and the asymptotical stability of square-mean almost periodic solutions to such nonautonomous stochastic differential equations. As an application, almost periodic solution to a concrete nonautonomous stochastic integro-differential equation is considered to illustrate the applicability of our abstract results.
ISSN:1439-8516
1439-7617
DOI:10.1007/s10114-013-1109-4