On almost periodic mild solutions for stochastic functional differential equations

• Published in: Nonlinear analysis: real world applications Vol. 13; no. 1; pp. 275 - 286
• Main Authors: Cao, Junfei, Yang, Qigui, Huang, Zaitang
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.02.2012
• Subjects: Differential equations; Mathematical analysis; Nonlinearity; Operators; Quadratic-mean almost periodic solution; Stability; Stochastic functional differential equations; Stochasticity; Quadratic-mean almost periodic solution; Stability; Stochastic functional differential equations
• ISSN: 1468-1218; 1878-5719
• DOI: 10.1016/j.nonrwa.2011.07.032

In this paper, a class of stochastic functional differential equations given by d x ( t ) = ( A x ( t ) + F ( t , x ( t ) , x t ) ) d t + G ( t , x ( t ) , x t ) ∘ d ω ( t ) , t ∈ [ 0 , T ] , x ( t ) = φ ( t ) for t ∈ [ − σ , 0 ] , is investigated. Under some suitable assumptions, the existence and stability of quadratic-mean almost periodic mild solutions for the equations are discussed by means of semigroups of operators and fixed point method. Moreover, an example is given to illustrate our results.