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