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July 2020 Finitary isomorphisms of Brownian motions
Zemer Kosloff, Terry Soo
Ann. Probab. 48(4): 1966-1979 (July 2020). DOI: 10.1214/19-AOP1412

Abstract

Ornstein and Shields (Advances in Math. 10 (1973) 143–146) 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 $q$.

Citation

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Zemer Kosloff. Terry Soo. "Finitary isomorphisms of Brownian motions." Ann. Probab. 48 (4) 1966 - 1979, July 2020. https://doi.org/10.1214/19-AOP1412

Information

Received: 1 June 2019; Revised: 1 October 2019; Published: July 2020
First available in Project Euclid: 20 July 2020

zbMATH: 07224965
MathSciNet: MR4124530
Digital Object Identifier: 10.1214/19-AOP1412

Subjects:
Primary: 37A35, 60G15, 60G55, 60J10

Rights: Copyright © 2020 Institute of Mathematical Statistics

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Vol.48 • No. 4 • July 2020
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