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 $\ge$ 0} is a one-dimensional Brownian motion, then {Bt -- 2 inf s$\le$t Bs, t $\ge$ 0} is a three dimensional Bessel process, i.e. a Brownia…