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Stochastics
An International Journal of Probability and Stochastic Processes
Volume 95, 2023 - Issue 1
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Research Article

Tempered exponential dichotomies for linear random evolution equations

, , &
Pages 1-22 | Received 06 May 2021, Accepted 21 Jan 2022, Published online: 10 Feb 2022
 

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.

AMS CLASSIFICATIONS:

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).

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