Matsumoto–Yor Process and Infinite Dimensional Hyperbolic Space

  • Philippe Bougerol
Part of the Lecture Notes in Mathematics book series (LNM, volume 2137)


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.


Brownian Motion Symmetric Space Hyperbolic Space Radial Part Maximal Compact Subgroup 
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© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Laboratoire de Probabilités et Modèles AléatoiresUniversité Pierre et Marie CurieParisFrance

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