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Finitary isomorphisms of Brownian motions
- Source :
- Ann. Probab. 48, no. 4 (2020), 1966-1979
- Publication Year :
- 2020
- Publisher :
- The Institute of Mathematical Statistics, 2020.
-
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.<br />Published at https://doi.org/10.1214/19-AOP1412 in the Annals of Probability by the Institute of Mathematical Statistics
- Subjects :
- Statistics and Probability
37A35
Rational number
Pure mathematics
renewal point processes
Dynamical Systems (math.DS)
finitary isomorphisms
Bernoulli's principle
Mathematics::Probability
reflected Brownian motions
FOS: Mathematics
Finitary
Almost surely
Mathematics - Dynamical Systems
Brownian motion
Mathematics
37A35, 60G15, 60G55, 60J10
Probability (math.PR)
Ornstein theory
Flow (mathematics)
Bounded function
60G15
60J10
Isomorphism
60G55
Statistics, Probability and Uncertainty
Mathematics - Probability
Subjects
Details
- Language :
- English
- Database :
- OpenAIRE
- Journal :
- Ann. Probab. 48, no. 4 (2020), 1966-1979
- Accession number :
- edsair.doi.dedup.....6a2d4bbaf7b8fdcc770d95ded276c22b