Stepanov-like pseudo almost periodicity in distribution and optimal control to impulsive partial stochastic differential equations

This paper concerns the Stepanov-like pseudo almost periodicity in distribution for a stochastic process and optimal control. Using the analytic semigroup theory, fractional power operators, stochastic analysis theory and fixed point strategy, we obtain the existence of Stepanov-like pseudo almost periodic in distribution mild solutions for impulsive partial stochastic functional differential equations under non-Lipschitz conditions. The existence of optimal pairs of system governed by impulsive partial stochastic control systems is also presented. Finally, an example is given for demonstration.