dc.contributor.author Veillette, Mark en_US dc.contributor.author Taqqu, Murad S. en_US dc.date.accessioned 2019-08-28T13:34:06Z dc.date.available 2019-08-28T13:34:06Z dc.date.issued 2010-04 dc.identifier http://www.sciencedirect.com/science/article/pii/S0167715210000039 dc.identifier.citation Mark Veillette, Murad S Taqqu. 2010. "Using differential equations to obtain joint moments of first-passage times of increasing Lévy processes." Statistics & Probability Letters, Volume 80, pp. 697 - 705. https://doi.org/10.1016/j.spl.2010.01.002 dc.identifier.issn 0167-7152 dc.identifier.uri https://hdl.handle.net/2144/37423 dc.description.abstract Let D(s),s≥0 be a Lévy subordinator, that is, a non-decreasing process with stationary and independent increments and suppose that D(0)=0. We study the first-hitting time of the process D, namely, the process E(t)=infs:D(s)\textgreatert, t≥0. The process E is, in general, non-Markovian with non-stationary and non-independent increments. We derive a partial differential equation for the Laplace transform of the n-time tail distribution function P[E(t1)\textgreaters1,…,E(tn)\textgreatersn]. This PDE can be used to derive all n-time moments of the process E. As an application, we give a recursive formula for multiple-time moments of the local time of a Markov process in terms of its transition density. en_US dc.format.extent 697 - 705 en_US dc.relation.ispartof Statistics & Probability Letters dc.subject Statistics & probability en_US dc.subject Mathematics en_US dc.subject Applied mathematics en_US dc.subject Statistics en_US dc.subject Econometrics en_US dc.title Using differential equations to obtain joint moments of first-passage times of increasing Lévy processes en_US dc.type Article en_US dc.description.version First author draft en_US dc.identifier.doi 10.1016/j.spl.2010.01.002 pubs.elements-source manual-entry en_US pubs.notes urldate: 2018-05-24 en_US pubs.notes Embargo: Not known en_US pubs.organisational-group Boston University en_US pubs.organisational-group Boston University, College of Arts & Sciences en_US pubs.organisational-group Boston University, College of Arts & Sciences, Department of Mathematics & Statistics en_US pubs.publication-status Published en_US dc.identifier.orcid 0000-0002-1145-9082 (Taqqu, Murad S) dc.identifier.mycv 54254
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