Existence Results for Some Stochastic Differential Equations

Paul H. Bezandry () and Toka Diagana ()
Additional contact information
Paul H. Bezandry: Howard University, Department of Mathematics
Toka Diagana: Howard University, Department of Mathematics

Chapter Chapter 5 in Almost Periodic Stochastic Processes, 2011, pp 129-142 from Springer

Abstract: Abstract Chapter 5 is devoted to the study of the existence of p-th mean almost periodic solutions to some classes of nonautonomous stochastic differential equations of type $$dX(t)=A(t)X(t)dt + F(t, X(t))dt + G(t, X(t))d\mathbb{W}(t), \ \ t \in \mathbb{R},$$ where $$(A(t))_{t \in \mathbb{R}}$$ is a family of densely defined closed linear operators satisfying the wellknown Acquistapace-Terreni conditions, $$F : \mathbb{R} \times L^p (\Omega, \mathbb{H}) \to L^p (\Omega, \mathbb{H}) \ {\rm and} \ G : \mathbb{R} \times L^p (\Omega, \mathbb{H}) \to L^p(\Omega, \mathbb{L}^{0}_{2})$$ are jointly continuous satisfying some additional conditions, and $$\mathbb{W}$$ is a Q-Wiener process with values in $$\mathbb{K}$$ . Some sufficient conditions for the existence of p-th mean almost periodic solutions to the autonomous counterpart of the above equation are also obtained. Finally, an analysis of some N-dimensional parabolic stochastic partial differential equations is provided to illustrate the applicability of our abstract results.

Date: 2011
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4419-9476-9_5

Ordering information: This item can be ordered from
http://www.springer.com/9781441994769

DOI: 10.1007/978-1-4419-9476-9_5

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().