Some two-dimensional extensions of Bougerol's identity in law for the exponential functional of linear Brownian motion

Jean Bertoin (1) , Daniel Dufresne (2) , Marc Yor (3, 4)

1 Institut für Mathematik [Zürich]
2 Centre of Actuarial Studies [Melbourne]
3 LPMA - Laboratoire de Probabilités et Modèles Aléatoires
4 IUF - Institut universitaire de France

We present a two-dimensional extension of an identity in distribution due to Bougerol \cite{Bou} that involves the exponential functional of a linear Brownian motion. Even though this identity does not extend at the level of processes, we point at further striking relations in this direction.

Mots clés: Brownian motion; exponential functional; Bougerol's identity; local time; Bessel processes.; Bessel processes

Domaines: Probabilités [math.PR]

Jean Bertoin, Daniel Dufresne, Marc Yor. Some two-dimensional extensions of Bougerol's identity in law for the exponential functional of linear Brownian motion. 2012. ⟨hal-00657538⟩