Tempered exponential dichotomies for linear random evolution equations

Abstract

This paper is concerned with the tempered exponential dichotomy for random differential systems in Banach spaces. Based on the presentation of bounded solutions for a tempered exponential dichotomous system, we give a bound under which the tempered exponentially dichotomous property of perturbed systems is preserved. Some applications of our results to stochastic partial differential equations are considered.

Keywords:

• Random dynamical systems
• semigroup
• generator
• tempered exponential dichotomy
• co-cycle

AMS CLASSIFICATIONS:

• 34D10
• 35R60
• 37H30
• 60H10

Acknowledgments

We gratefully thank the reviewer and the editor for constructive comments and detailed suggestions, which led to much improvement of the presentation of the paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).