Open Access
July 2024 Datko type characterizations for exponential instability in average of cocycles
Tian Yue
Author Affiliations +
Hiroshima Math. J. 54(2): 219-232 (July 2024). DOI: 10.32917/h2023003

Abstract

In this paper, we consider the problem of exponential instability behavior of random dynamical systems described by cocycles in Banach spaces. We prove some continuous and discrete versions of Datko type theorem for the exponential instability in average of cocycles. In addition, two characterizations of the exponential instability in average in terms of Lyapunov functions are given.

Funding Statement

This work is supported by the Natural Science Foundation of Hubei Province of China (Grant Nos. 2022CFB457, 2022CFB538) and the Industry-University Cooperation Collaborative Education Project of Ministry of Education (Grant Nos. 202002137038, 202101301022).

Acknowledgments

The author is sincerely grateful to the editor and the referee for carefully reading the manuscript and for valuable suggestions which led to the improvement of this paper.

Citation

Download Citation

Tian Yue. "Datko type characterizations for exponential instability in average of cocycles." Hiroshima Math. J. 54 (2) 219 - 232, July 2024. https://doi.org/10.32917/h2023003

Information

Received: 14 March 2023; Revised: 11 September 2023; Published: July 2024
First available in Project Euclid: 18 July 2024

Digital Object Identifier: 10.32917/h2023003

Subjects:
Primary: 37H30 , 37L55
Secondary: 34D05

Keywords: Cocycle , Datko type characterization , exponential instability in average , Lyapunov function

Rights: Copyright © 2024 Hiroshima University, Mathematics Program

Vol.54 • No. 2 • July 2024
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