ABSTRACT
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.
Acknowledgments
The authors would like to thank the editor and the reviewer for their constructive comments and suggestions.
Disclosure statement
No potential conflict of interest was reported by the author(s).