Show simple item record

dc.contributor.authorAvram, Florinen_US
dc.contributor.authorTaqqu, Murad S.en_US
dc.date.accessioned2018-09-05T18:39:43Z
dc.date.available2018-09-05T18:39:43Z
dc.date.issued1992-01-01
dc.identifierhttps://projecteuclid.org/euclid.aop/1176989938
dc.identifier.citationF. Avram, M.S. Taqqu. 1992. "Weak Convergence of Sums of Moving Averages in the α -Stable Domain of Attraction." The Annals of Probability, Volume 20, Issue 1, pp. 483 - 503 (21). https://doi.org/10.1214/aop/1176989938
dc.identifier.issn0091-1798
dc.identifier.urihttps://hdl.handle.net/2144/31176
dc.description.abstractSkorohod has shown that the convergence of sums of i.i.d. random variables to an a-stable Levy motion, with 0 < a < 2, holds in the weak-J1 sense. J1 is the commonly used Skorohod topology. We show that for sums of moving averages with at least two nonzero coefficients, weak-J1 conver- gence cannot hold because adjacent jumps of the process can coalesce in the limit; however, if the moving average coefficients are positive, then the adjacent jumps are essentially monotone and one can have weak-M1 con- vergence. M1 is weaker than J1, but it is strong enough for the sup and inf functionals to be continuous.en_US
dc.format.extent483 - 503 (21)en_US
dc.languageEnglish
dc.publisherINST MATHEMATICAL STATISTICSen_US
dc.relation.ispartofThe Annals of Probability
dc.relation.isversionofhttps://doi.org/10.1214/aop/1176989938
dc.rights© 1992 Institute of Mathematical Statisticsen_US
dc.subjectScience & technologyen_US
dc.subjectPhysical sciencesen_US
dc.subjectStatistics & probabilityen_US
dc.subjectMathematicsen_US
dc.subjectTopological theoremsen_US
dc.subjectStaircasesen_US
dc.subjectPerceptron convergence procedureen_US
dc.subjectMathematical theoremsen_US
dc.subjectCounterexamplesen_US
dc.subjectStochastic processesen_US
dc.subjectStatisticsen_US
dc.titleWeak convergence of sums of moving averages in the α-stable domain of attractionen_US
dc.typeArticleen_US
pubs.elements-sourcemanual-entryen_US
pubs.notesArticles older than 3 years are OA: https://projecteuclid.org/euclid.aopen_US
pubs.notesEmbargo: 36 monthsen_US
pubs.notesArticles are OA after 3 years https://projecteuclid.org/euclid.aopen_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, MS)


This item appears in the following Collection(s)

Show simple item record