Null flows, positive flows and the structure of stationary symmetric stable processes
Probability
2007-05-23 v1
Abstract
This paper elucidates the connection between stationary symmetric alpha-stable processes with 0<alpha<2 and nonsingular flows on measure spaces by describing a new and unique decomposition of stationary stable processes into those corresponding to positive flows and those corresponding to null flows. We show that a necessary and sufficient for a stationary stable process to be ergodic is that its positive component vanishes.
Keywords
Cite
@article{arxiv.math/0412419,
title = {Null flows, positive flows and the structure of stationary symmetric stable processes},
author = {Gennady Samorodnitsky},
journal= {arXiv preprint arXiv:math/0412419},
year = {2007}
}