Revista Matemática Iberoamericana


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Volume 29, Issue 4, 2013, pp. 1307–1324
DOI: 10.4171/RMI/758

Published online: 2013-12-15

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

Jean Bertoin[1], Daniel Dufresne[2] and Marc Yor

(1) Universität Zürich, Switzerland
(2) University of Melbourne, Melbourne, Australia

We present a two-dimensional extension of an identity in distribution due to Bougerol [4] that involves the exponential functional of a linear Brownian motion. Even though this identity does not extend to the level of processes, we point out further striking relations in this direction.

Keywords: Brownian motion, exponential functional, Bougerol’s identity, local time, Bessel processes

Bertoin Jean, Dufresne Daniel, Yor Marc: Some two-dimensional extensions of Bougerol’s identity in law for the exponential functional of linear Brownian motion. Rev. Mat. Iberoam. 29 (2013), 1307-1324. doi: 10.4171/RMI/758