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Article: On the maximum of randomly weighted sums with regularly varying tails

TitleOn the maximum of randomly weighted sums with regularly varying tails
Authors
KeywordsAsymptotics
Regular variation
Ruin probability
Tail probability
Issue Date2006
PublisherElsevier BV. The Journal's web site is located at http://www.elsevier.com/locate/stapro
Citation
Statistics And Probability Letters, 2006, v. 76 n. 10, p. 971-975 How to Cite?
AbstractConsider the randomly weighted sums Sn(θ) = ∑k=1 n θkXk, n = 1,2,..., where {Xk, k = 1, 2,...} is a sequence of independent real-valued random variables with common distribution F, whose right tail is regularly varying with exponent - α < 0, and {θk, k = 1,2,...} is a sequence of positive random variables, independent of {Xk, k = 1,2,...}. Under a suitable summability condition on the upper endpoints of θk, k = 1, 2,..., we prove that Pr(max1≤n<∞ Sn(θ) > x) ∼ F̄(x)∑k=1 ∞ Eθk α. © 2005 Elsevier B.V. All rights reserved.
Persistent Identifierhttp://hdl.handle.net/10722/82657
ISSN
2015 Impact Factor: 0.506
2015 SCImago Journal Rankings: 0.720
ISI Accession Number ID
References

 

DC FieldValueLanguage
dc.contributor.authorChen, Yen_HK
dc.contributor.authorNg, KWen_HK
dc.contributor.authorXie, Xen_HK
dc.date.accessioned2010-09-06T08:31:55Z-
dc.date.available2010-09-06T08:31:55Z-
dc.date.issued2006en_HK
dc.identifier.citationStatistics And Probability Letters, 2006, v. 76 n. 10, p. 971-975en_HK
dc.identifier.issn0167-7152en_HK
dc.identifier.urihttp://hdl.handle.net/10722/82657-
dc.description.abstractConsider the randomly weighted sums Sn(θ) = ∑k=1 n θkXk, n = 1,2,..., where {Xk, k = 1, 2,...} is a sequence of independent real-valued random variables with common distribution F, whose right tail is regularly varying with exponent - α < 0, and {θk, k = 1,2,...} is a sequence of positive random variables, independent of {Xk, k = 1,2,...}. Under a suitable summability condition on the upper endpoints of θk, k = 1, 2,..., we prove that Pr(max1≤n<∞ Sn(θ) > x) ∼ F̄(x)∑k=1 ∞ Eθk α. © 2005 Elsevier B.V. All rights reserved.en_HK
dc.languageengen_HK
dc.publisherElsevier BV. The Journal's web site is located at http://www.elsevier.com/locate/staproen_HK
dc.relation.ispartofStatistics and Probability Lettersen_HK
dc.rightsStatistics & Probability Letters. Copyright © Elsevier BV.en_HK
dc.subjectAsymptoticsen_HK
dc.subjectRegular variationen_HK
dc.subjectRuin probabilityen_HK
dc.subjectTail probabilityen_HK
dc.titleOn the maximum of randomly weighted sums with regularly varying tailsen_HK
dc.typeArticleen_HK
dc.identifier.openurlhttp://library.hku.hk:4550/resserv?sid=HKU:IR&issn=0167-7152&volume=76&issue=10&spage=971&epage=975&date=2006&atitle=On+the+maximum+of+randomly+weighted+sums+with+regularly+varying+tailsen_HK
dc.identifier.emailNg, KW: kaing@hkucc.hku.hken_HK
dc.identifier.authorityNg, KW=rp00765en_HK
dc.description.naturelink_to_subscribed_fulltext-
dc.identifier.doi10.1016/j.spl.2005.10.033en_HK
dc.identifier.scopuseid_2-s2.0-33645550697en_HK
dc.identifier.hkuros119418en_HK
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-33645550697&selection=ref&src=s&origin=recordpageen_HK
dc.identifier.volume76en_HK
dc.identifier.issue10en_HK
dc.identifier.spage971en_HK
dc.identifier.epage975en_HK
dc.identifier.isiWOS:000237155900001-
dc.publisher.placeNetherlandsen_HK
dc.identifier.scopusauthoridChen, Y=36468032600en_HK
dc.identifier.scopusauthoridNg, KW=7403178774en_HK
dc.identifier.scopusauthoridXie, X=23111436500en_HK

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