1. Finitary isomorphisms of Brownian motions
- Author
-
Zemer Kosloff and Terry Soo
- 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 - 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., Published at https://doi.org/10.1214/19-AOP1412 in the Annals of Probability by the Institute of Mathematical Statistics
- Published
- 2020