Header

UZH-Logo

Maintenance Infos

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


Bertoin, Jean; Dufresne, Daniel; Yor, Marc (2013). Some two-dimensional extensions of Bougerol’s identity in law for the exponential functional of linear Brownian motion. Revista matemática iberoamericana, 29(4):1307-1324.

Abstract

The main result is a two-dimensional identity in law. Let (B t ,L t ) and (β t ,λ t ) be two independent pairs of a linear Brownian motion with its local time at 0. Let A t =∫ 0 t exp(2B s )ds. Then, for fixed t, the pair (sinh(B t ),sinh(L t )) has the same law as (β(A t ),exp(-B t )λ(A t )), and also as (exp(-B t )β(A t ),λ(A t )). This result is an extension of an identity in distribution due to Bougerol that concerned the first components of each pair. Some other related identities are also considered.

Abstract

The main result is a two-dimensional identity in law. Let (B t ,L t ) and (β t ,λ t ) be two independent pairs of a linear Brownian motion with its local time at 0. Let A t =∫ 0 t exp(2B s )ds. Then, for fixed t, the pair (sinh(B t ),sinh(L t )) has the same law as (β(A t ),exp(-B t )λ(A t )), and also as (exp(-B t )β(A t ),λ(A t )). This result is an extension of an identity in distribution due to Bougerol that concerned the first components of each pair. Some other related identities are also considered.

Statistics

Citations

Dimensions.ai Metrics
3 citations in Web of Science®
3 citations in Scopus®
4 citations in Microsoft Academic
Google Scholar™

Altmetrics

Downloads

0 downloads since deposited on 30 Sep 2014
0 downloads since 12 months

Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:2013
Deposited On:30 Sep 2014 14:41
Last Modified:05 Jul 2018 10:44
Publisher:Universidad de La Rioja ; Dialnet
ISSN:0213-2230
OA Status:Green
Publisher DOI:https://doi.org/10.4171/RMI/758
Related URLs:https://dialnet.unirioja.es/servlet/articulo?codigo=4626233 (Publisher)
Other Identification Number:arXiv:1201.1495

Download

Download PDF  'Some two-dimensional extensions of Bougerol’s identity in law for the exponential functional of linear Brownian motion'.
Preview
Content: Accepted Version
Filetype: PDF
Size: 243kB
View at publisher