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arXiv · 1905.07867

Finitary isomorphisms of Brownian motions

Zemer Kosloff·Terry Soo
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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.

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Zemer Kosloff, Terry Soo. 2019-05-20. Finitary isomorphisms of Brownian motions. https://doi.org/10.1214/19-aop1412

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