Pseudo almost periodic in distribution solutions to impulsive partial stochastic functional differential equations. (English) Zbl 1502.34092
Summary: In this paper, we study the piecewise pseudo almost periodicity in distribution for a stochastic process. Using the analytic semigroup theory and fixed point strategy with stochastic analysis theory, we obtain the existence and the exponential stability of piecewise pseudo almost periodic in distribution mild solutions for impulsive partial neutral stochastic functional differential equations under non-Lipschitz conditions. Moreover, an example is given to illustrate the general theorems.
MSC:
| 34K50 | Stochastic functional-differential equations |
| 34K30 | Functional-differential equations in abstract spaces |
| 34K45 | Functional-differential equations with impulses |
| 34K14 | Almost and pseudo-almost periodic solutions to functional-differential equations |
| 43A60 | Almost periodic functions on groups and semigroups and their generalizations (recurrent functions, distal functions, etc.); almost automorphic functions |
| 47N20 | Applications of operator theory to differential and integral equations |
Keywords:
impulsive partial stochastic functional differential equations; piecewise pseudo almost periodic functions; pseudo almost periodic in distribution; analytic semigroup theory; fixed pointReferences:
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