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

The Hebrew University of Jerusalem

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	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

Keywords

Finitary isomorphisms
Ornstein theory
Reflected brownian motions
Renewal point processes

All Science Journal Classification (ASJC) codes

Statistics and Probability
Statistics, Probability and Uncertainty

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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.

AB - 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.

KW - Finitary isomorphisms

KW - Ornstein theory

KW - Reflected brownian motions

KW - Renewal point processes

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DO - 10.1214/19-AOP1412

M3 - مقالة

SN - 0091-1798

VL - 48

SP - 1966

EP - 1979

JO - Annals of Probability

JF - Annals of Probability

IS - 4

ER -

Finitary isomorphisms of Brownian motions

Abstract

Keywords

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