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2015 | OriginalPaper | Buchkapitel

Matsumoto–Yor Process and Infinite Dimensional Hyperbolic Space

verfasst von : Philippe Bougerol

Erschienen in: In Memoriam Marc Yor - Séminaire de Probabilités XLVII

Verlag: Springer International Publishing

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Abstract

The Matsumoto–Yor process is \(\int _{0}^{t}\exp (2B_{s} - B_{t})\,ds,t \geq 0\), where (B _t) is a Brownian motion. It is shown that it is the limit of the radial part of the Brownian motion at the bottom of the spectrum on the hyperbolic space of dimension q, when q tends to infinity. Analogous processes on infinite series of non compact symmetric spaces and on regular trees are described.

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Titel: Matsumoto–Yor Process and Infinite Dimensional Hyperbolic Space
verfasst von: Philippe Bougerol
Verlag: Springer International Publishing
Buch: In Memoriam Marc Yor - Séminaire de Probabilités XLVII
Print ISBN: 978-3-319-18584-2

Electronic ISBN: 978-3-319-18585-9

Copyright-Jahr: 2015
DOI: https://doi.org/10.1007/978-3-319-18585-9_23