The joint law of the last zeros of Brownian motion and of its Lévy transform

The joint study of functionals of a Brownian motion $B$ and its Lévy transform $\beta= |B|-L$, where $L$ is the local time of $B$ at zero, is motivated by the conjectured ergodicity of the Lévy transform. Here, we compute explicitly the covariance of the last zeros before time one of $B$ and $\beta$...

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Bibliographic Details
Published in:Ergodic theory and dynamical systems 2000-06, Vol.20 (3), p.709-725
Main Authors: DONATI-MARTIN, CATHERINE, SHI, ZHAN, YOR, MARC
Format: Article
Language:English
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Summary:The joint study of functionals of a Brownian motion $B$ and its Lévy transform $\beta= |B|-L$, where $L$ is the local time of $B$ at zero, is motivated by the conjectured ergodicity of the Lévy transform. Here, we compute explicitly the covariance of the last zeros before time one of $B$ and $\beta$, which turns out to be strictly positive.
ISSN:0143-3857
1469-4417
DOI:10.1017/S0143385700000389