Density estimates for jump diffusion processes

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• dc.contributor.author Kohatsu-Higa, Arturo
• dc.contributor.author Nualart, Eulàlia
• dc.contributor.author Tran, Ngoc Khue
• dc.date.accessioned 2022-05-17T09:23:28Z
• dc.date.available 2022-05-17T09:23:28Z
• dc.date.issued 2022
• dc.description.abstract 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.
• dc.description.sponsorship 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.
• dc.format.mimetype application/pdf
• dc.identifier.citation Kohatsu-Higa A, Nualart E, Tran Nk. Density estimates for jump diffusion processes. Applied Mathematics and Computation. 2022 May;420:126814. DOI: 10.1016/j.amc.2021.126814
• dc.identifier.doi http://dx.doi.org/10.1016/j.amc.2021.126814
• dc.identifier.issn 0096-3003
• dc.identifier.uri http://hdl.handle.net/10230/53112
• dc.language.iso eng
• dc.publisher Elsevier
• dc.relation.ispartof Applied Mathematics and Computation. 2022 May;420:126814
• dc.relation.projectID info:eu-repo/grantAgreement/ES/2PE/PGC2018-101643-B-I00
• dc.rights © 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/).
• dc.rights.accessRights info:eu-repo/semantics/openAccess
• dc.rights.uri http://creativecommons.org/licenses/by-nc-nd/4.0/
• dc.subject.keyword Density estimates
• dc.subject.keyword Jump diffusion process
• dc.subject.keyword Malliavin calculus
• dc.title Density estimates for jump diffusion processes
• dc.type info:eu-repo/semantics/article
• dc.type.version info:eu-repo/semantics/publishedVersion