On Bougerol and Dufresne's identities for exponential Brownian functionals
type: Item
instance of: scholarly article
title: On Bougerol and Dufresne's identities for exponential Brownian functionals
zbMATH Open document ID: 0942.60063
author: Hiroyuki Matsumoto
author: Marc Yor
published in: Proceedings of the Japan Academy. Series A
publication date: 2000-08-16T00:00:00Z
review text: The note contains several new distributional identities involving exponential functionals of the Brownian motion \(B=(B_t)\) and closely related with results by Bougerol and Dufresne. E.g., it is shown that the distribution of the following two-dimensional random vectors coincide: \(({\mathbf e}e^{-B_t}A_t,B_t)\) and \((\cosh(|B_t|+L_t),B_t)\) where \(A_t=\int_0^te^{2B_s}ds\), \(L\) is the local time of \(B\) at zero, and \({\mathbf e}\) is an exponential random variable independent of \(B\).
Mathematics Subject Classification ID: 60J65
zbMATH DE Number: 1275058
zbMATH Keywords: Brownian motion
zbMATH Keywords: local time
zbMATH Keywords: Bessel process
zbMATH Keywords: exponential functional
zbMATH Keywords: distributional identities
zbMATH Keywords: Bougerol identity
reviewed by: Yuri Kabanov
MaRDI profile type: Publication
full work available at URL: pjaa.74.152
OpenAlex ID: W2003457804
cites work: Q4395530
cites work: Q3316270
cites work: Diffusion in a one-dimensional random medium and hyperbolic Brownian motion
cites work: Exponential functionals of Brownian motion and disordered systems
cites work: The Distribution of a Perpetuity, with Applications to Risk Theory and Pension Funding
cites work: An affine property of the reciprocal Asian option process
cites work: Semi-groupe du mouvement brownienhyperbolique
cites work: Brownian motion on the hyperbolic plane and Selberg trace formula
cites work: Q4279447
cites work: Une approche unifiee pour une forme exacte dU prix d'une option dans les differents modeles a volatilite stochastique
cites work: Q4303982
cites work: On some exponential functionals of Brownian motion
cites work: Q4012542
cites work: Q4349251
cites work: Q4383826
DOI: 10.3792/PJAA.74.152
description: scientific article; zbMATH DE number 1275058