Stable stationary processes related to cyclic flows
Abstract
We study stationary stable processes related to periodic and cyclic flows in the sense of Rosinski [Ann. Probab. 23 (1995) 1163-1187]. These processes are not ergodic. We provide their canonical representations, consider examples and show how to identify them among general stationary stable processes. We conclude with the unique decomposition in distribution of stationary stable processes into the sum of four major independent components: 1. A mixed moving average component. 2. A harmonizable (or ``trivial'') component. 3. A cyclic component 4. A component which is different from these.
Cite
@article{arxiv.math/0410114,
title = {Stable stationary processes related to cyclic flows},
author = {Vladas Pipiras and Murad S. Taqqu},
journal= {arXiv preprint arXiv:math/0410114},
year = {2016}
}
Comments
Published by the Institute of Mathematical Statistics (http://www.imstat.org) in the Annals of Probability (http://www.imstat.org/aop/) at http://dx.doi.org/10.1214/009117904000000108