Ratio ergodic theorems: From Hopf to Birkhoff and Kingman
Dynamical Systems
2018-02-26 v1 Probability
Abstract
Hopf's ratio ergodic theorem has an inherent symmetry which we exploit to provide a simplification of standard proofs of Hopf's and Birkhoff's ergodic theorems. We also present a ratio ergodic theorem for conservative transformations on a -finite measure space, generalizing Kingman's ergodic theorem for subadditive sequences and generalizing previous results by Akcoglu and Sucheston.
Keywords
Cite
@article{arxiv.1802.08439,
title = {Ratio ergodic theorems: From Hopf to Birkhoff and Kingman},
author = {Hans Henrik Rugh and Damien Thomine},
journal= {arXiv preprint arXiv:1802.08439},
year = {2018}
}