Pseudo almost periodic in distribution solutions to impulsive partial stochastic functional differential equations

ABSTRACT

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.

KEYWORDS:

• Impulsive partial stochastic functional differential equations
• piecewise pseudo almost periodic functions
• Pseudo almost periodic in distribution
• analytic semigroup theory
• fixed point

2010 MR SUBJECT CLASSIFICATIONS:

• 34A37
• 60H10
• 35B15
• 34F05

Acknowledgments

The authors would like to thank the editor and the reviewers for their constructive comments and suggestions.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work is supported by the National Natural Science Foundation of China (11461019), the President Fund of Scientific Research Innovation and Application of Hexi University (xz2013-10).