Asymptotically Almost Periodic Solutions for a Class of Stochastic Functional Differential Equations
Joint Authors
Liu, Aimin
Liu, Yongjian
Liu, Qun
Source
Issue
Vol. 2014, Issue 2014 (31 Dec. 2014), pp.1-11, 11 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2014-05-06
Country of Publication
Egypt
No. of Pages
11
Main Subjects
Abstract EN
This work is concerned with the quadratic-mean asymptotically almost periodic mild solutions for a class of stochastic functional differential equations d x t = A t x t + F t , x t , x t d t + H ( t , x t , x t ) ∘ d W ( t ) .
A new criterion ensuring the existence and uniqueness of the quadratic-mean asymptotically almost periodic mild solutions for the system is presented.
The condition of being uniformly exponentially stable of the strongly continuous semigroup { T t } t ≥ 0 is essentially removed, which is generated by the linear densely defined operator A ∶ D ( A ) ⊂ L 2 ( ℙ , ℍ ) → L 2 ( ℙ , ℍ ) , only using the exponential trichotomy of the system, which reflects a deeper analysis of the behavior of solutions of the system.
In this case the asymptotic behavior is described through the splitting of the main space into stable, unstable, and central subspaces at each point from the flow’s domain.
An example is also given to illustrate our results.
American Psychological Association (APA)
Liu, Aimin& Liu, Yongjian& Liu, Qun. 2014. Asymptotically Almost Periodic Solutions for a Class of Stochastic Functional Differential Equations. Abstract and Applied Analysis،Vol. 2014, no. 2014, pp.1-11.
https://search.emarefa.net/detail/BIM-1015093
Modern Language Association (MLA)
Liu, Aimin…[et al.]. Asymptotically Almost Periodic Solutions for a Class of Stochastic Functional Differential Equations. Abstract and Applied Analysis No. 2014 (2014), pp.1-11.
https://search.emarefa.net/detail/BIM-1015093
American Medical Association (AMA)
Liu, Aimin& Liu, Yongjian& Liu, Qun. Asymptotically Almost Periodic Solutions for a Class of Stochastic Functional Differential Equations. Abstract and Applied Analysis. 2014. Vol. 2014, no. 2014, pp.1-11.
https://search.emarefa.net/detail/BIM-1015093
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1015093