Density estimates for jump diffusion processes

We consider a real-valued diffusion process with a linear jump term driven by a Poisson point process and we assume that the jump amplitudes have a centered density with finite moments. We show upper and lower estimates for the density of the solution in the case that the jump amplitudes follow a Ga...

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Autores: Kohatsu-Higa, Arturo, Nualart, Eulàlia, Tran, Ngoc Khue
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2022
País:España
Institución:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
Repositorio:Recercat. Dipósit de la Recerca de Catalunya
OAI Identifier:oai:recercat.cat:10230/53112
Acceso en línea:http://hdl.handle.net/10230/53112
http://dx.doi.org/10.1016/j.amc.2021.126814
Access Level:acceso abierto
Palabra clave:Density estimates
Jump diffusion process
Malliavin calculus
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spelling Density estimates for jump diffusion processesKohatsu-Higa, ArturoNualart, EulàliaTran, Ngoc KhueDensity estimatesJump diffusion processMalliavin calculusWe consider a real-valued diffusion process with a linear jump term driven by a Poisson point process and we assume that the jump amplitudes have a centered density with finite moments. We show upper and lower estimates for the density of the solution in the case that the jump amplitudes follow a Gaussian or Laplacian law. The proof of the lower bound uses a general expression for the density of the solution in terms of the convolution of the density of the continuous part and the jump amplitude density. The upper bound uses an upper tail estimate in terms of the jump amplitude distribution and techniques of the Malliavin calculus in order to bound the density by the tails of the solution. We also extend the lower bounds to the multidimensional case.Eulalia Nualart acknowledges support from the Spanish MINECO grant PGC2018-101643-B-I00 and Ayudas Fundacion BBVA a Equipos de Investigación Científica 2017. Ngoc Khue Tran acknowledges support from the Vietnam Institute for Advanced Study in Mathematics (VIASM ) where a part of this work was done during his visit.Elsevier202220222022info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfapplication/pdfhttp://hdl.handle.net/10230/53112http://dx.doi.org/10.1016/j.amc.2021.126814reponame:Recercat. Dipósit de la Recerca de Catalunyainstname:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)InglésApplied Mathematics and Computation. 2022 May;420:126814info:eu-repo/grantAgreement/ES/2PE/PGC2018-101643-B-I00© 2021 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).http://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessoai:recercat.cat:10230/531122026-05-29T05:05:01Z
dc.title.none.fl_str_mv Density estimates for jump diffusion processes
title Density estimates for jump diffusion processes
spellingShingle Density estimates for jump diffusion processes
Kohatsu-Higa, Arturo
Density estimates
Jump diffusion process
Malliavin calculus
title_short Density estimates for jump diffusion processes
title_full Density estimates for jump diffusion processes
title_fullStr Density estimates for jump diffusion processes
title_full_unstemmed Density estimates for jump diffusion processes
title_sort Density estimates for jump diffusion processes
dc.creator.none.fl_str_mv Kohatsu-Higa, Arturo
Nualart, Eulàlia
Tran, Ngoc Khue
author Kohatsu-Higa, Arturo
author_facet Kohatsu-Higa, Arturo
Nualart, Eulàlia
Tran, Ngoc Khue
author_role author
author2 Nualart, Eulàlia
Tran, Ngoc Khue
author2_role author
author
dc.subject.none.fl_str_mv Density estimates
Jump diffusion process
Malliavin calculus
topic Density estimates
Jump diffusion process
Malliavin calculus
description We consider a real-valued diffusion process with a linear jump term driven by a Poisson point process and we assume that the jump amplitudes have a centered density with finite moments. We show upper and lower estimates for the density of the solution in the case that the jump amplitudes follow a Gaussian or Laplacian law. The proof of the lower bound uses a general expression for the density of the solution in terms of the convolution of the density of the continuous part and the jump amplitude density. The upper bound uses an upper tail estimate in terms of the jump amplitude distribution and techniques of the Malliavin calculus in order to bound the density by the tails of the solution. We also extend the lower bounds to the multidimensional case.
publishDate 2022
dc.date.none.fl_str_mv 2022
2022
2022
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/10230/53112
http://dx.doi.org/10.1016/j.amc.2021.126814
url http://hdl.handle.net/10230/53112
http://dx.doi.org/10.1016/j.amc.2021.126814
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Applied Mathematics and Computation. 2022 May;420:126814
info:eu-repo/grantAgreement/ES/2PE/PGC2018-101643-B-I00
dc.rights.none.fl_str_mv http://creativecommons.org/licenses/by-nc-nd/4.0/
info:eu-repo/semantics/openAccess
rights_invalid_str_mv http://creativecommons.org/licenses/by-nc-nd/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
dc.source.none.fl_str_mv reponame:Recercat. Dipósit de la Recerca de Catalunya
instname:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
instname_str Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
reponame_str Recercat. Dipósit de la Recerca de Catalunya
collection Recercat. Dipósit de la Recerca de Catalunya
repository.name.fl_str_mv
repository.mail.fl_str_mv
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