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.
Bibliographical noteFunding Information:
Acknowledgments. We thank Benjy Weiss for helpful discussions and encouragement. We also thank Russell Lyons and Richard Bradley for their helpful comments regarding the Proof of Theorem 3. Finally, we thank the referee who provided many good suggestions. The first author was funded in part by ISF Grant No. 1570/17. The second author was funded in part by a General Research Fund, provided by the University of Kansas, where he was a faculty member.
© Institute of Mathematical Statistics, 2020.
- Finitary isomorphisms
- Ornstein theory
- Reflected brownian motions
- Renewal point processes