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math.PR2018
Pitman transforms and Brownian motion in the interval viewed as an affine alcove
Philippe Bougerol, Manon Defosseux
Pitman's theorem states that if {Bt, t 0} is a one-dimensional Brownian motion, then {Bt -- 2 inf st Bs, t 0} is a three dimensional Bessel process, i.e. a Brownia…
math.PR2014★ 4 cited
The Matsumoto and Yor process and infinite dimensional hyperbolic space
Philippe Bougerol
The Matsumoto\,--Yor process is , where is a Brownian motion. It is shown that it is the limit of the radial part of the Brownian motion a…