Baudoin, Fabrice and O’Connell, Neil. (2011) Exponential functionals of Brownian motion and class-one Whittaker functions. Annales de l'Institut Henri Poincaré, Probabilités et Statistiques, Vol.47 (No.4). pp. 1096-1120. ISSN 0246-0203

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Abstract

We consider exponential functionals of a Brownian motion with drift in R(n), defined via a collection of linear functionals. We give a characterisation of the Laplace transform of their joint law as the unique bounded solution, up to a constant factor, to a Schrodinger-type partial differential equation. We derive a similar equation for the probability density. We then characterise all diffusions which can be interpreted as having the law of the Brownian motion with drift conditioned on the law of its exponential functionals. In the case where the family of linear functionals is a set of simple roots, the Laplace transform of the joint law of the corresponding exponential functionals can be expressed in terms of a (class-one) Whittaker function associated with the corresponding root system. In this setting, we establish some basic properties of the corresponding diffusion processes.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science > Mathematics
Journal or Publication Title:	Annales de l'Institut Henri Poincaré, Probabilités et Statistiques
Publisher:	Institute of Mathematical Statistics
ISSN:	0246-0203
Date:	2011
Volume:	Vol.47
Number:	No.4
Number of Pages:	25
Page Range:	pp. 1096-1120
Identification Number:	10.1214/10-AIHP401
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access
URI:	http://wrap.warwick.ac.uk/id/eprint/39650

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