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Frequently hypercyclic random vectors for $C_{0}$-semigroups

Part of: Ergodic theory Stochastic analysis General theory of linear operators

Published online by Cambridge University Press:  18 February 2026

KEVIN AGNEESSENS Open the ORCID record for KEVIN AGNEESSENS [Opens in a new window]
KEVIN AGNEESSENS*
Affiliation:
Département de mathématiques, Université de Mons , Belgium
*
e-mail: agneessens.kevin@gmail.com
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Abstract

We show that, under certain conditions, a strongly continuous semigroup admits an almost surely frequently hypercyclic random vector defined as a stochastic integral in Fréchet spaces with respect to the Brownian motion. Two criteria are given. We will apply the second criterion to three examples: translation semigroups on spaces of integrable functions, the exponential of weighted shifts, and the translation operators on the space of entire functions. This last example, with a stochastic approach, seems to be new in the literature. Some other examples are given.

Keywords

frequent hypercyclicitysemigroup of operatorsergodic theorystochastic integral

MSC classification

Primary: 47A16: Cyclic vectors, hypercyclic and chaotic operators 37A10: One-parameter continuous families of measure-preserving transformations
Secondary: 60H05: Stochastic integrals

Information

Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 46 , Issue 5 , May 2026 , pp. 1125 - 1154
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Copyright
© The Author(s), 2026. Published by Cambridge University Press

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