Finitary isomorphisms of Brownian motions
Dynamical Systems
2020-07-23 v3 Probability
Abstract
Ornstein and Shields (Advances in Math., 10:143-146, 1973) proved that Brownian motion reflected on a bounded region is an infinite entropy Bernoulli flow and thus Ornstein theory yielded the existence of a measure-preserving isomorphism between any two such Brownian motions. For fixed h >0, we construct by elementary methods, isomorphisms with almost surely finite coding windows between Brownian motions reflected on the intervals [0, qh] for all positive rationals q.
Keywords
Cite
@article{arxiv.1905.07867,
title = {Finitary isomorphisms of Brownian motions},
author = {Zemer Kosloff and Terry Soo},
journal= {arXiv preprint arXiv:1905.07867},
year = {2020}
}
Comments
Published at https://doi.org/10.1214/19-AOP1412 in the Annals of Probability by the Institute of Mathematical Statistics