Pseudo Almost Periodic Solutions to Impulsive Non-autonomous Stochastic Differential Equations with Unbounded Delay and its Optimal Control

This paper is concerned with the pseudo almost periodic in distribution mild solutions for impulsive non-autonomous stochastic differential equations with unbounded delay and optimal controls in Hilbert spaces. Firstly, a suitable pseudo almost periodic in distribution mild solutions is introduced. The existence of pseudo almost periodic in distribution mild solutions are proved by means of a fixed-point theorem for condensing maps combined with stochastic analysis theory and evolution family. Secondly, the existence of optimal pairs of system governed by impulsive non-autonomous stochastic differential equations is also presented. Finally, an example is given for demonstration.