Distributional limits of positive, ergodic stationary processes and infinite ergodic transformations
Dynamical Systems
2021-04-14 v3 Probability
Abstract
In this note we identify the distributional limits of non-negative, ergodic stationary processes, showing that all are possible. Consequences for infinite ergodic theory are also explored and new examples of distributionally stable- and -rationally ergodic tranformations are presented.
Cite
@article{arxiv.1604.03218,
title = {Distributional limits of positive, ergodic stationary processes and infinite ergodic transformations},
author = {Jon. Aaronson and Benjamin Weiss},
journal= {arXiv preprint arXiv:1604.03218},
year = {2021}
}
Comments
added considerations of "bounded rational ergodicity" as "$\infty$- rational ergodicity"