Existence and global attractiveness of a pseudo almost periodic solution in p-th mean sense for stochastic evolution equation driven by a fractional Brownian motion

Abstract

In this work, we establish a new concept of pseudo almost periodic processes in p-th mean sense using the measure theory. We use the μ-ergodic process to define the spaces of μ-pseudo almost periodic process in the p-th mean sense. We establish many interesting results on the functional space of such processes like completeness and composition theorems. The main objective of this paper is to use those results and some stochastic analysis approaches to study the existence, the uniqueness and the global attractiveness for a μ-pseudo almost periodic mild solution to a class of abstract stochastic evolution equations driven by fractional Brownian motion. We provide an example to illustrate our results.

Keywords::

• measure theory
• ergodicity
• μ-pseudo almost periodic solution
• completeness
• composition theorem
• stochastic processes
• stochastic evolution equations

AMS Subject Classification::

• 34C27
• 34K14
• 34K30
• 34K50
• 35B15
• 35K55
• 60G20

Acknowledgements

The authors express sincere gratitude to the referee for his remarks which helped us a lot to improve the original version of this work.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

^1. Email: [email protected]

^2. Email: [email protected]