Existence and stability of almost periodic solutions to impulsive stochastic differential equations. (English) Zbl 1292.34054
Summary: This paper introduces the concept of square-mean piecewise almost periodicity for impulsive stochastic processes. The existence of square-mean piecewise almost periodic solutions for linear and nonlinear impulsive stochastic differential equations is established by using the theory of the semigroups of operators and Schauder’s fixed point theorem. The stability of the square-mean piecewise almost periodic solutions for nonlinear impulsive stochastic differential equations is investigated.
MSC:
| 34F05 | Ordinary differential equations and systems with randomness |
| 34A37 | Ordinary differential equations with impulses |
| 34C27 | Almost and pseudo-almost periodic solutions to ordinary differential equations |
| 34D20 | Stability of solutions to ordinary differential equations |
| 47N20 | Applications of operator theory to differential and integral equations |
| 60H15 | Stochastic partial differential equations (aspects of stochastic analysis) |
| 37C75 | Stability theory for smooth dynamical systems |
