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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.

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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 Apr 2016 18:23
Publisher:European Mathematical Society Publishing House
ISSN:2235-0616
Free access at:Publisher DOI. An embargo period may apply.
Publisher DOI:https://doi.org/10.4171/RMI/758

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