Random Walks Whose Concave Majorants Often Have Few Faces

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dc.contributor.authorQiao, Zhihua
dc.contributor.authorSteele, J Michael
dc.date2023-05-17T18:03:13.000
dc.date.accessioned2023-05-23T03:34:08Z
dc.date.available2023-05-23T03:34:08Z
dc.date.issued2005-11-15
dc.date.submitted2017-09-07T12:29:10-07:00
dc.description.abstractWe construct a continuous distribution G such that the number of faces in the smallest concave majorant of the random walk with G-distributed summands will take on each natural number infinitely often with probability one. This investigation is motivated by the fact that the number of faces Fn of the concave majorant of the random walk at time n has the same distribution as the number of records Rn in the sequence of summands up to time n. Since Rn is almost surely asymptotic to log n, the construction shows that despite the equality of all of the one-dimensional marginals, the almost sure behaviors of the sequences { Rn } and { Fn } may be radically different.
dc.identifier.urihttps://repository.upenn.edu/handle/20.500.14332/47515
dc.legacy.articleid1592
dc.legacy.fields10.1016/j.spl.2005.05.012
dc.legacy.fulltexturlhttps://repository.upenn.edu/cgi/viewcontent.cgi?article=1592&context=statistics_papers&unstamped=1
dc.source.beginpage97
dc.source.endpage102
dc.source.issue16
dc.source.issue2
dc.source.journalStatistics Papers
dc.source.journaltitleStatistics & Probability Letters
dc.source.peerreviewedtrue
dc.source.statuspublished
dc.source.volume75
dc.subject.otherSpitzer's combinatorial lemma
dc.subject.otherRandom walk
dc.subject.otherConvex hull
dc.subject.otherConvex minorant
dc.subject.otherConcave majorant
dc.subject.otherBusiness
dc.subject.otherStatistics and Probability
dc.titleRandom Walks Whose Concave Majorants Often Have Few Faces
dc.typeArticle
digcom.identifierstatistics_papers/16
digcom.identifier.contextkey10721908
digcom.identifier.submissionpathstatistics_papers/16
digcom.typearticle
dspace.entity.typePublication
upenn.schoolDepartmentCenterStatistics Papers
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