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

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.

Keywords:

• Impulsive partial stochastic functional differential equations
• Stepanov-like pseudo almost periodicity in distribution
• optimal control
• analytic semigroup theory
• fixed point

2010 MR Subject Classifications:

• 34A37
• 60H15
• 35B15
• 34F05

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).

Additional information

Funding

This work is supported by the National Natural Science Foundation of China (11461019).