A scaling proof for Walsh's Brownian motion extended arc-sine law

We present a new proof of the extended arc-sine law related to Walsh's Brownian motion, known also as Brownian spider. The main argument mimics the scaling property used previously, in particular by D. Williams in the 1-dimensional Brownian case, which can be generalized to the multivariate case. A discussion concerning the time spent positive by a skew Bessel process is also presented.

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Source https://hal.science/hal-00708858
Author Vakeroudis, Stavros, Yor, Marc
Maintainer CCSD
Last Updated May 29, 2026, 05:54 (UTC)
Created May 29, 2026, 05:54 (UTC)
Identifier hal-00708858
Language en
Rights https://about.hal.science/hal-authorisation-v1/
contributor Probability and Actuarial Sciences group ; Département de Mathématique [Bruxelles] (ULB) ; Faculté des Sciences [Bruxelles] (ULB) ; Université libre de Bruxelles = Free University of Brussels (ULB)-Université libre de Bruxelles = Free University of Brussels (ULB)-Faculté des Sciences [Bruxelles] (ULB) ; Université libre de Bruxelles = Free University of Brussels (ULB)-Université libre de Bruxelles = Free University of Brussels (ULB)
creator Vakeroudis, Stavros
date 2012-06-15T00:00:00
harvest_object_id 7fd7d4d0-029c-4f8e-9a0c-53f0fd66c3b9
harvest_source_id 3374d638-d20b-4672-ba96-a23232d55657
harvest_source_title test moissonnage SELUNE
metadata_modified 2026-01-28T00:00:00
relation info:eu-repo/semantics/altIdentifier/arxiv/1206.3688
set_spec type:UNDEFINED