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dc.contributor.authorVeillette, Marken_US
dc.contributor.authorTaqqu, Murad S.en_US
dc.date.accessioned2019-08-28T13:57:12Z
dc.date.available2019-08-28T13:57:12Z
dc.date.issued2010-12-01
dc.identifierhttp://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000283614400011&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=6e74115fe3da270499c3d65c9b17d654
dc.identifier.citationMark Veillette, Murad S Taqqu. 2010. "Numerical Computation of First-Passage Times of Increasing Levy Processes." METHODOLOGY AND COMPUTING IN APPLIED PROBABILITY, Volume 12, Issue 4, pp. 695 - 729 (35). https://doi.org/10.1007/s11009-009-9158-y
dc.identifier.issn1387-5841
dc.identifier.issn1573-7713
dc.identifier.urihttps://hdl.handle.net/2144/37428
dc.description.abstractLet {D(s), s ≥ 0} be a non-decreasing Lévy process. The first-hitting time process {E(t), t ≥ 0} (which is sometimes referred to as an inverse subordinator) defined by 𝐸(𝑡)=inf{𝑠:𝐷(𝑠)>𝑡} is a process which has arisen in many applications. Of particular interest is the mean first-hitting time 𝑈(𝑡)=𝔼𝐸(𝑡) . This function characterizes all finite-dimensional distributions of the process E. The function U can be calculated by inverting the Laplace transform of the function 𝑈˜(𝜆)=(𝜆𝜙(𝜆))−1 , where ϕ is the Lévy exponent of the subordinator D. In this paper, we give two methods for computing numerically the inverse of this Laplace transform. The first is based on the Bromwich integral and the second is based on the Post-Widder inversion formula. The software written to support this work is available from the authors and we illustrate its use at the end of the paper.en_US
dc.description.sponsorshipThis research was partially supported by the NSF grants DMS-0505747, DMS-0706786, and DGE-0221680. (DMS-0505747 - NSF; DMS-0706786 - NSF; DGE-0221680 - NSF)en_US
dc.format.extent695 - 729 (35)en_US
dc.languageEnglish
dc.publisherSPRINGERen_US
dc.relation.ispartofMETHODOLOGY AND COMPUTING IN APPLIED PROBABILITY
dc.subjectStatistics & probabilityen_US
dc.subjectMathematicsen_US
dc.subjectLévy subordinatorsen_US
dc.subjectFirst-hitting timesen_US
dc.subjectPost-Widder methoden_US
dc.subjectNumerical inversion of transformsen_US
dc.subjectAnomalous diffusionen_US
dc.subjectJump processesen_US
dc.subjectApplied mathematicsen_US
dc.subjectNumerical and computational mathematicsen_US
dc.subjectStatisticsen_US
dc.titleNumerical computation of first-passage times of increasing Lévy processesen_US
dc.typeArticleen_US
dc.description.versionFirst author draften_US
dc.identifier.doi10.1007/s11009-009-9158-y
pubs.elements-sourceweb-of-scienceen_US
pubs.notesEmbargo: Not knownen_US
pubs.organisational-groupBoston Universityen_US
pubs.organisational-groupBoston University, College of Arts & Sciencesen_US
pubs.organisational-groupBoston University, College of Arts & Sciences, Department of Mathematics & Statisticsen_US
pubs.publication-statusPublisheden_US
dc.identifier.orcid0000-0002-1145-9082 (Taqqu, Murad S)
dc.identifier.mycv54253


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