2014/08/09 by Philippe Bougerol, Bougerol, Philippe
Mathematics · #FOS: Mathematics #Probability (math.PR) #math.PR
paper · pdf · doi:10.48550/arxiv.1408.2108
32
arxiv created 2015/02/06 · arxiv updated 2015/02/09
The Matsumoto --Yor process is ∫_0t exp(2B_s-B_t) ds, 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.