Finitary isomorphisms of Brownian motions

Zemer Kosloff; Terry Soo

doi:10.1214/19-AOP1412

Finitary isomorphisms of Brownian motions

Zemer Kosloff, Terry Soo

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

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 measurepreserving 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.

Original language	American English
Pages (from-to)	1966-1979
Number of pages	14
Journal	Annals of Probability
Volume	48
Issue number	4
DOIs	https://doi.org/10.1214/19-AOP1412
State	Published - 1 Jul 2020

Bibliographical note

Funding Information:
Acknowledgments. We thank Benjy Weiss for helpful discussions and encouragement. We also thank Russell Lyons and Richard Bradley for their helpful comments regarding the Proof of Theorem 3. Finally, we thank the referee who provided many good suggestions. The first author was funded in part by ISF Grant No. 1570/17. The second author was funded in part by a General Research Fund, provided by the University of Kansas, where he was a faculty member.

Publisher Copyright:
© Institute of Mathematical Statistics, 2020.

Keywords

Finitary isomorphisms
Ornstein theory
Reflected brownian motions
Renewal point processes

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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 measurepreserving 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.",

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N2 - 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 measurepreserving 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.

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KW - Renewal point processes

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Finitary isomorphisms of Brownian motions

Abstract

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Keywords

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