Finitary isomorphisms of Brownian motions

Zemer Kosloff, Terry Soo

Research output: Contribution to journalArticlepeer-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 languageAmerican English
Pages (from-to)1966-1979
Number of pages14
JournalAnnals of Probability
Volume48
Issue number4
DOIs
StatePublished - 1 Jul 2020

Bibliographical note

Publisher Copyright:
© Institute of Mathematical Statistics, 2020.

Keywords

  • Finitary isomorphisms
  • Ornstein theory
  • Reflected brownian motions
  • Renewal point processes

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