\(p\)-th mean pseudo almost automorphic mild solutions to some nonautonomous stochastic differential equations. (English) Zbl 1246.34056

Bezandry, P. H.; Diagana, T.

Afr. Diaspora J. Math. 12, No. 1, 60-79 (2011).

Summary: We first introduce and study the concepts of \(p\)-th mean pseudo almost automorphy and that of \(p\)-th mean pseudo almost periodicity for \(p \geq 2\). Next, we make extensive use of the well-known Schauder’s fixed point principle to obtain the existence of \(p\)-th mean pseudo almost automorphic mild solutions to some nonautonomous stochastic differential equations.

MSC:

34G10	Linear differential equations in abstract spaces
60H10	Stochastic ordinary differential equations (aspects of stochastic analysis)
34F05	Ordinary differential equations and systems with randomness
47N20	Applications of operator theory to differential and integral equations
43A60	Almost periodic functions on groups and semigroups and their generalizations (recurrent functions, distal functions, etc.); almost automorphic functions

Keywords:

stochastic differential equation; square-mean pseudo almost automorphic; \(p\)-th mean pseudo almost automorphic; \(p\)-th mean pseudo almost periodic; square-mean pseudo almost periodic; Wiener process