Fluctuations of Stable Processes and Exponential Functionals of Hypergeometric Lévy Processes

We study the distribution and various properties of exponential functionals of hypergeometric Levy processes. We derive an explicit formula for the Mellin transform of the exponential functional and give both convergent and asymptotic series expansions of its probability density function. As applica...

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Detalles Bibliográficos
Autor: JUAN CARLOS PARDO MILLAN
Tipo de recurso: informe técnico
Estado:Versión publicada
Fecha de publicación:2010
País:México
Institución:Centro de Investigación en Matemáticas
Repositorio:Repositorio Institucional CIMAT
Idioma:inglés
OAI Identifier:oai:cimat.repositorioinstitucional.mx:1008/606
Acceso en línea:http://cimat.repositorioinstitucional.mx/jspui/handle/1008/606
Access Level:acceso abierto
Palabra clave:info:eu-repo/classification/MSC/Procesos de Levy
info:eu-repo/classification/cti/1
info:eu-repo/classification/cti/12
info:eu-repo/classification/cti/1208
info:eu-repo/classification/cti/120806
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spelling Fluctuations of Stable Processes and Exponential Functionals of Hypergeometric Lévy ProcessesJUAN CARLOS PARDO MILLANinfo:eu-repo/classification/MSC/Procesos de Levyinfo:eu-repo/classification/cti/1info:eu-repo/classification/cti/12info:eu-repo/classification/cti/1208info:eu-repo/classification/cti/120806info:eu-repo/classification/cti/120806We study the distribution and various properties of exponential functionals of hypergeometric Levy processes. We derive an explicit formula for the Mellin transform of the exponential functional and give both convergent and asymptotic series expansions of its probability density function. As applications we present a new proof of some of the results on the density of the supremum of a stable process, which were recently obtained in [25] and [23]. We also derive some new results related to (i) the entrance law of the stable process conditioned to stay positive, (ii) the entrance law of the excursion measure of the stable process re ected at its past in mum and (iii) the entrance law and the last passage time of the radial part of n-dimensional symmetric stable process.Centro de Investigación en Matemáticas AC2010-12-01info:eu-repo/semantics/reportinfo:eu-repo/semantics/publishedVersionapplication/pdfhttp://cimat.repositorioinstitucional.mx/jspui/handle/1008/606reponame:Repositorio Institucional CIMATinstname:Centro de Investigación en Matemáticasinstacron:CIMATenginfo:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by-nc/4.0oai:cimat.repositorioinstitucional.mx:1008/6062024-08-27T22:38:51Z
dc.title.none.fl_str_mv Fluctuations of Stable Processes and Exponential Functionals of Hypergeometric Lévy Processes
title Fluctuations of Stable Processes and Exponential Functionals of Hypergeometric Lévy Processes
spellingShingle Fluctuations of Stable Processes and Exponential Functionals of Hypergeometric Lévy Processes
JUAN CARLOS PARDO MILLAN
info:eu-repo/classification/MSC/Procesos de Levy
info:eu-repo/classification/cti/1
info:eu-repo/classification/cti/12
info:eu-repo/classification/cti/1208
info:eu-repo/classification/cti/120806
info:eu-repo/classification/cti/120806
title_short Fluctuations of Stable Processes and Exponential Functionals of Hypergeometric Lévy Processes
title_full Fluctuations of Stable Processes and Exponential Functionals of Hypergeometric Lévy Processes
title_fullStr Fluctuations of Stable Processes and Exponential Functionals of Hypergeometric Lévy Processes
title_full_unstemmed Fluctuations of Stable Processes and Exponential Functionals of Hypergeometric Lévy Processes
title_sort Fluctuations of Stable Processes and Exponential Functionals of Hypergeometric Lévy Processes
dc.creator.none.fl_str_mv JUAN CARLOS PARDO MILLAN
author JUAN CARLOS PARDO MILLAN
author_facet JUAN CARLOS PARDO MILLAN
author_role author
dc.subject.none.fl_str_mv info:eu-repo/classification/MSC/Procesos de Levy
info:eu-repo/classification/cti/1
info:eu-repo/classification/cti/12
info:eu-repo/classification/cti/1208
info:eu-repo/classification/cti/120806
info:eu-repo/classification/cti/120806
topic info:eu-repo/classification/MSC/Procesos de Levy
info:eu-repo/classification/cti/1
info:eu-repo/classification/cti/12
info:eu-repo/classification/cti/1208
info:eu-repo/classification/cti/120806
info:eu-repo/classification/cti/120806
description We study the distribution and various properties of exponential functionals of hypergeometric Levy processes. We derive an explicit formula for the Mellin transform of the exponential functional and give both convergent and asymptotic series expansions of its probability density function. As applications we present a new proof of some of the results on the density of the supremum of a stable process, which were recently obtained in [25] and [23]. We also derive some new results related to (i) the entrance law of the stable process conditioned to stay positive, (ii) the entrance law of the excursion measure of the stable process re ected at its past in mum and (iii) the entrance law and the last passage time of the radial part of n-dimensional symmetric stable process.
publishDate 2010
dc.date.none.fl_str_mv 2010-12-01
dc.type.none.fl_str_mv info:eu-repo/semantics/report
info:eu-repo/semantics/publishedVersion
format report
status_str publishedVersion
dc.identifier.none.fl_str_mv http://cimat.repositorioinstitucional.mx/jspui/handle/1008/606
url http://cimat.repositorioinstitucional.mx/jspui/handle/1008/606
dc.language.none.fl_str_mv eng
language eng
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
http://creativecommons.org/licenses/by-nc/4.0
eu_rights_str_mv openAccess
rights_invalid_str_mv http://creativecommons.org/licenses/by-nc/4.0
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Centro de Investigación en Matemáticas AC
publisher.none.fl_str_mv Centro de Investigación en Matemáticas AC
dc.source.none.fl_str_mv reponame:Repositorio Institucional CIMAT
instname:Centro de Investigación en Matemáticas
instacron:CIMAT
instname_str Centro de Investigación en Matemáticas
instacron_str CIMAT
institution CIMAT
reponame_str Repositorio Institucional CIMAT
collection Repositorio Institucional CIMAT
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15.812429

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