FINITARY ISOMORPHISMS OF BROWNIAN MOTIONS

• 成果类型: Article
• 署名作者: Kosloff, Zemer; Soo, Terry
• 署名单位: Hebrew University of Jerusalem; University of London; University College London
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/19-AOP1412
• 发表日期: 2020
• 页码: 1966-1979
• 关键词: bernoulli-shifts; entropy; invariant; CODES; extension; square

摘要

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 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.