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dc.contributor.authorSalins, Michaelen_US
dc.contributor.authorSpiliopoulos, Konstantinosen_US
dc.date.accessioned2019-03-06T18:32:51Z
dc.date.available2019-03-06T18:32:51Z
dc.date.issued2017-12-01
dc.identifierhttp://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000407735800002&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=6e74115fe3da270499c3d65c9b17d654
dc.identifier.citationMichael Salins, Konstantinos Spiliopoulos. 2017. "Markov processes with spatial delay: Path space characterization, occupation time and properties." STOCHASTICS AND DYNAMICS, Volume 17, Issue 6, pp. ? - ? (21). https://doi.org/10.1142/S0219493717500423
dc.identifier.issn0219-4937
dc.identifier.issn1793-6799
dc.identifier.urihttps://hdl.handle.net/2144/34252
dc.description.abstractIn this paper, we study one-dimensional Markov processes with spatial delay. Since the seminal work of Feller, we know that virtually any one-dimensional, strong, homogeneous, continuous Markov process can be uniquely characterized via its infinitesimal generator and the generator’s domain of definition. Unlike standard diffusions like Brownian motion, processes with spatial delay spend positive time at a single point of space. Interestingly, the set of times that a delay process spends at its delay point is nowhere dense and forms a positive measure Cantor set. The domain of definition of the generator has restrictions involving second derivatives. In this paper we provide a pathwise characterization for processes with delay in terms of an SDE and an occupation time formula involving the symmetric local time. This characterization provides an explicit Doob–Meyer decomposition, demonstrating that such processes are semi-martingales and that all of stochastic calculus including Itô formula and Girsanov formula applies. We also establish an occupation time formula linking the time that the process spends at a delay point with its symmetric local time there. A physical example of a stochastic dynamical system with delay is lastly presented and analyzed.en_US
dc.description.sponsorshipWe would like to thank Professor Ioannis Karatzas for making known to us, upon completion of this work, of the recent results of [2, 3]. The present work was partially supported by NSF Grant DMS-1312124 and during revisions of this paper by NSF CAREER award DMS 1550918. (DMS-1312124 - NSF; DMS 1550918 - NSF CAREER award)en_US
dc.format.extent21 p.en_US
dc.languageEnglish
dc.language.isoen_US
dc.publisherWORLD SCIENTIFIC PUBL CO PTE LTDen_US
dc.relation.ispartofSTOCHASTICS AND DYNAMICS
dc.subjectScience & technologyen_US
dc.subjectPhysical sciencesen_US
dc.subjectStatistics & probabilityen_US
dc.subjectMathematicsen_US
dc.subjectMarkov processesen_US
dc.subjectDelay pointsen_US
dc.subjectSticky pointsen_US
dc.subjectDynamical systemsen_US
dc.subjectFeller characterizationen_US
dc.subjectGeneralized operatorsen_US
dc.subjectOccupation timeen_US
dc.subjectNarrow domainsen_US
dc.subjectStochastic differential-equationsen_US
dc.subjectSticky brownian-motionen_US
dc.subjectDiffusionen_US
dc.subjectApplied mathematicsen_US
dc.subjectNumerical and computational mathematicsen_US
dc.subjectStatisticsen_US
dc.subjectStatistics & probabilityen_US
dc.titleMarkov processes with spatial delay: path space characterization, occupation time and propertiesen_US
dc.typeArticleen_US
dc.description.versionAccepted manuscripten_US
dc.identifier.doi10.1142/S0219493717500423
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


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