ASYMPTOTIC EXPECTED NUMBER OF PASSAGES OF A RANDOM WALK THROUGH AN INTERVAL

DC FieldValueLanguage
dc.contributor.authorKella, Offer
dc.contributor.authorStadje, Wolfgang
dc.date.accessioned2021-12-23T16:11:35Z-
dc.date.available2021-12-23T16:11:35Z-
dc.date.issued2013
dc.identifier.issn00219002
dc.identifier.urihttps://osnascholar.ub.uni-osnabrueck.de/handle/unios/9781-
dc.description.abstractIn this note we find a new result concerning the asymptotic expected number of passages of a finite or infinite interval (x, x h] as x -> infinity for a random walk with increments having a positive expected value. If the increments are distributed like X then the limit for 0 < h < infinity turns out to have the form E min(vertical bar X vertical bar, h)/EX, which unexpectedly is independent of h for the special case where vertical bar X vertical bar <= b < infinity almost surely and h > b. When h = infinity, the limit is E max(X, 0)/EX. For the case of a simple random walk, a more pedestrian derivation of the limit is given.
dc.description.sponsorshipIsrael Science FoundationIsrael Science Foundation [434/09]; Vigevani Chair in Statistics; Deutsche ForschungsgemeinschaftGerman Research Foundation (DFG) [306/13-2]; Supported in part by grant no. 434/09 from the Israel Science Foundation and the Vigevani Chair in Statistics.; Supported by grant no. 306/13-2 of the Deutsche Forschungsgemeinschaft
dc.language.isoen
dc.publisherCAMBRIDGE UNIV PRESS
dc.relation.ispartofJOURNAL OF APPLIED PROBABILITY
dc.subjectgeneralized renewal theorem
dc.subjectMathematics
dc.subjectpassage
dc.subjectRandom walk
dc.subjectStatistics & Probability
dc.subjecttwo-sided renewal theorem
dc.titleASYMPTOTIC EXPECTED NUMBER OF PASSAGES OF A RANDOM WALK THROUGH AN INTERVAL
dc.typejournal article
dc.identifier.isiISI:000322206200020
dc.description.volume50
dc.description.issue1
dc.description.startpage288
dc.description.endpage294
dc.identifier.eissn14756072
dc.publisher.placeEDINBURGH BLDG, SHAFTESBURY RD, CB2 8RU CAMBRIDGE, ENGLAND
dcterms.isPartOf.abbreviationJ. Appl. Probab.
crisitem.author.deptFB 06 - Mathematik/Informatik-
crisitem.author.deptidfb06-
crisitem.author.parentorgUniversität Osnabrück-
crisitem.author.netidStWo325-
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