Level sets of multiparameter Brownian motions

We use Girsanov's theorem to establish a conjecture of Khoshnevisan, Xiao and Zhong that ϕ(r)=rN−d/2(loglog(1r))d/2 is the exact Hausdorff measure function for the zero level set of an N-parameter d-dimensional additive Brownian motion. We extend this result to a natural multiparameter vers...

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Detalles Bibliográficos
Autores: Nualart, Eulàlia, Mountford, Thomas S.
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2004
País:España
Institución:Universitat Pompeu Fabra
Repositorio:Repositorio Digital de la UPF
OAI Identifier:oai:repositori.upf.edu:10230/34388
Acceso en línea:http://hdl.handle.net/10230/34388
http://dx.doi.org/10.1214/EJP.v9-169
Access Level:acceso abierto
Palabra clave:Local times
Hausdorff measure
Level sets
Additive Brownian motion
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spelling Level sets of multiparameter Brownian motionsNualart, EulàliaMountford, Thomas S.Local timesHausdorff measureLevel setsAdditive Brownian motionWe use Girsanov's theorem to establish a conjecture of Khoshnevisan, Xiao and Zhong that ϕ(r)=rN−d/2(loglog(1r))d/2 is the exact Hausdorff measure function for the zero level set of an N-parameter d-dimensional additive Brownian motion. We extend this result to a natural multiparameter version of Taylor and Wendel's theorem on the relationship between Brownian local time and the Hausdorff ϕ-measure of the zero set.The research of Mountford TS is partially supported by the NSF Grant DMS. The research of Nualart E is supported by the Fonds National Suisse.Institute of Mathematical Statistics (IMS)201820182004info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfapplication/pdfhttp://hdl.handle.net/10230/34388http://dx.doi.org/10.1214/EJP.v9-169reponame:Repositorio Digital de la UPFinstname:Universitat Pompeu FabraInglésElectronic Journal of Probability. 2004;9(20):594-614.This article is published with a Creative Commons Attribution Licence (CC BY 2.5)http://creativecommons.org/licenses/by/2.5/legalcodeinfo:eu-repo/semantics/openAccessoai:repositori.upf.edu:10230/343882026-06-12T07:21:37Z
dc.title.none.fl_str_mv Level sets of multiparameter Brownian motions
title Level sets of multiparameter Brownian motions
spellingShingle Level sets of multiparameter Brownian motions
Nualart, Eulàlia
Local times
Hausdorff measure
Level sets
Additive Brownian motion
title_short Level sets of multiparameter Brownian motions
title_full Level sets of multiparameter Brownian motions
title_fullStr Level sets of multiparameter Brownian motions
title_full_unstemmed Level sets of multiparameter Brownian motions
title_sort Level sets of multiparameter Brownian motions
dc.creator.none.fl_str_mv Nualart, Eulàlia
Mountford, Thomas S.
author Nualart, Eulàlia
author_facet Nualart, Eulàlia
Mountford, Thomas S.
author_role author
author2 Mountford, Thomas S.
author2_role author
dc.subject.none.fl_str_mv Local times
Hausdorff measure
Level sets
Additive Brownian motion
topic Local times
Hausdorff measure
Level sets
Additive Brownian motion
description We use Girsanov's theorem to establish a conjecture of Khoshnevisan, Xiao and Zhong that ϕ(r)=rN−d/2(loglog(1r))d/2 is the exact Hausdorff measure function for the zero level set of an N-parameter d-dimensional additive Brownian motion. We extend this result to a natural multiparameter version of Taylor and Wendel's theorem on the relationship between Brownian local time and the Hausdorff ϕ-measure of the zero set.
publishDate 2004
dc.date.none.fl_str_mv 2004
2018
2018
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/10230/34388
http://dx.doi.org/10.1214/EJP.v9-169
url http://hdl.handle.net/10230/34388
http://dx.doi.org/10.1214/EJP.v9-169
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Electronic Journal of Probability. 2004;9(20):594-614.
dc.rights.none.fl_str_mv This article is published with a Creative Commons Attribution Licence (CC BY 2.5)
http://creativecommons.org/licenses/by/2.5/legalcode
info:eu-repo/semantics/openAccess
rights_invalid_str_mv This article is published with a Creative Commons Attribution Licence (CC BY 2.5)
http://creativecommons.org/licenses/by/2.5/legalcode
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Institute of Mathematical Statistics (IMS)
publisher.none.fl_str_mv Institute of Mathematical Statistics (IMS)
dc.source.none.fl_str_mv reponame:Repositorio Digital de la UPF
instname:Universitat Pompeu Fabra
instname_str Universitat Pompeu Fabra
reponame_str Repositorio Digital de la UPF
collection Repositorio Digital de la UPF
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repository.mail.fl_str_mv
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