Skip to main content

Research Repository

Advanced Search

Random periodic processes, periodic measures and ergodicity

Feng, Chunrong; Zhao, Huaizhong

Random periodic processes, periodic measures and ergodicity Thumbnail


Authors



Abstract

Ergodicity of random dynamical systems with a periodic measure is obtained on a Polish space. In the Markovian case, the idea of Poincaré sections is introduced. It is proved that if the periodic measure is PS-ergodic, then it is ergodic. Moreover, if the infinitesimal generator of the Markov semigroup only has equally placed simple eigenvalues including 0 on the imaginary axis, then the periodic measure is PS-ergodic and has positive minimum period. Conversely if the periodic measure with the positive minimum period is PS-mixing, then the infinitesimal generator only has equally placed simple eigenvalues (infinitely many) including 0 on the imaginary axis. Moreover, under the spectral gap condition, PS-mixing of the periodic measure is proved. The “equivalence” of random periodic processes and periodic measures is established. This is a new class of ergodic random processes. Random periodic paths of stochastic perturbation of the periodic motion of an ODE is obtained.

Citation

Feng, C., & Zhao, H. (2020). Random periodic processes, periodic measures and ergodicity. Journal of Differential Equations, 269(9), 7382-7428. https://doi.org/10.1016/j.jde.2020.05.034

Journal Article Type Article
Acceptance Date May 31, 2020
Online Publication Date Jun 5, 2020
Publication Date 2020-10
Deposit Date Jan 5, 2021
Publicly Available Date Oct 6, 2021
Journal Journal of Differential Equations
Print ISSN 0022-0396
Publisher Elsevier
Peer Reviewed Peer Reviewed
Volume 269
Issue 9
Pages 7382-7428
DOI https://doi.org/10.1016/j.jde.2020.05.034

Files




You might also like



Downloadable Citations