Non-stationary It\^o-Kawada and Ergodic Theorems for random isometries
Dynamical Systems
2023-10-27 v1 Probability
Abstract
We consider a nonstationary sequence of independent random isometries of a compact metrizable space. Assuming that there are no proper closed subsets with deterministic image we establish a weak-* convergence to the unique invariant under isometries measure, Ergodic Theorem and Large Deviation Type Estimate. We also show that all the results can be carried over to the case of a random walk on a compact metrizable group. In particular, we prove a nonstationary analog of classical It\^o-Kawada theorem and give a new alternative proof for the stationary case.
Keywords
Cite
@article{arxiv.2310.17105,
title = {Non-stationary It\^o-Kawada and Ergodic Theorems for random isometries},
author = {Grigorii Monakov},
journal= {arXiv preprint arXiv:2310.17105},
year = {2023}
}
Comments
arXiv admin note: text overlap with arXiv:2307.05798