Please use this identifier to cite or link to this item: https://hdl.handle.net/10356/142214
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dc.contributor.authorFlint, Ianen_US
dc.contributor.authorPrivault, Nicolasen_US
dc.contributor.authorTorrisi, Giovanni Lucaen_US
dc.date.accessioned2020-06-17T07:04:27Z-
dc.date.available2020-06-17T07:04:27Z-
dc.date.issued2019-
dc.identifier.citationFlint, I., Privault, N., & Torrisi, G. L. (2019). Functional inequalities for marked point processes. Electronic Journal of Probability, 24, 116-. doi:10.1214/19-EJP369en_US
dc.identifier.issn1083-6489en_US
dc.identifier.urihttps://hdl.handle.net/10356/142214-
dc.description.abstractIn recent years, a number of functional inequalities have been derived for Poisson random measures, with a wide range of applications. In this paper, we prove that such inequalities can be extended to the setting of marked temporal point processes, under mild assumptions on their Papangelou conditional intensity. First, we derive a Poincaré inequality. Second, we prove two transportation cost inequalities. The first one refers to functionals of marked point processes with a Papangelou conditional intensity and is new even in the setting of Poisson random measures. The second one refers to the law of marked temporal point processes with a Papangelou conditional intensity, and extends a related inequality which is known to hold on a general Poisson space. Finally, we provide a variational representation of the Laplace transform of functionals of marked point processes with a Papangelou conditional intensity. The proofs make use of an extension of the Clark-Ocone formula to marked temporal point processes. Our results are shown to apply to classes of renewal, nonlinear Hawkes and Cox point processes.en_US
dc.description.sponsorshipMOE (Min. of Education, S’pore)en_US
dc.language.isoenen_US
dc.relation.ispartofElectronic Journal of Probabilityen_US
dc.rights© 2019 The Author(s) (published by The Institute of Mathematical Statistics and the Bernoulli Society). This is an open-access article distributed under the terms of the Creative Commons Attribution License.en_US
dc.subjectScience::Mathematicsen_US
dc.titleFunctional inequalities for marked point processesen_US
dc.typeJournal Articleen
dc.contributor.schoolSchool of Physical and Mathematical Sciencesen_US
dc.identifier.doi10.1214/19-EJP369-
dc.description.versionPublished versionen_US
dc.identifier.scopus2-s2.0-85074027426-
dc.identifier.volume24en_US
dc.subject.keywordsClark-Ocone Formulaen_US
dc.subject.keywordsMalliavin Calculusen_US
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