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Article: Precise large deviations for sums of random variables with consistently varying tails

TitlePrecise large deviations for sums of random variables with consistently varying tails
Authors
KeywordsConsistently varying tail
Doubly stochastic process
Heavy tail
Matuszewska index
Negative association
Precise large deviations
Random sums
Issue Date2004
PublisherApplied Probability Trust. The Journal's web site is located at http://www.shef.ac.uk/uni/companies/apt/ap.html
Citation
Journal Of Applied Probability, 2004, v. 41 n. 1, p. 93-107 How to Cite?
AbstractLet {Xk, k ≥ 1} be a sequence of independent, identically distributed nonnegative random variables with common distribution function F and finite expectation μ > 0. Under the assumption that the tail probability F̄(x) = 1 - F(x) is consistently varying as x tends to infinity, this paper investigates precise large deviations for both the partial sums Sn and the random sums SN(t), where N(·) is a counting process independent of the sequence {Xk, k ≥ 1}. The obtained results improve some related classical ones. Applications to a risk model with negatively associated claim occurrences and to a risk model with a doubly stochastic arrival process (extended Cox process) are proposed.
Persistent Identifierhttp://hdl.handle.net/10722/82856
ISSN
2015 Impact Factor: 0.665
2015 SCImago Journal Rankings: 0.742
ISI Accession Number ID
References

 

DC FieldValueLanguage
dc.contributor.authorNg, KWen_HK
dc.contributor.authorTang, Qen_HK
dc.contributor.authorYan, JAen_HK
dc.contributor.authorYang, Hen_HK
dc.date.accessioned2010-09-06T08:34:12Z-
dc.date.available2010-09-06T08:34:12Z-
dc.date.issued2004en_HK
dc.identifier.citationJournal Of Applied Probability, 2004, v. 41 n. 1, p. 93-107en_HK
dc.identifier.issn0021-9002en_HK
dc.identifier.urihttp://hdl.handle.net/10722/82856-
dc.description.abstractLet {Xk, k ≥ 1} be a sequence of independent, identically distributed nonnegative random variables with common distribution function F and finite expectation μ > 0. Under the assumption that the tail probability F̄(x) = 1 - F(x) is consistently varying as x tends to infinity, this paper investigates precise large deviations for both the partial sums Sn and the random sums SN(t), where N(·) is a counting process independent of the sequence {Xk, k ≥ 1}. The obtained results improve some related classical ones. Applications to a risk model with negatively associated claim occurrences and to a risk model with a doubly stochastic arrival process (extended Cox process) are proposed.en_HK
dc.languageengen_HK
dc.publisherApplied Probability Trust. The Journal's web site is located at http://www.shef.ac.uk/uni/companies/apt/ap.htmlen_HK
dc.relation.ispartofJournal of Applied Probabilityen_HK
dc.subjectConsistently varying tailen_HK
dc.subjectDoubly stochastic processen_HK
dc.subjectHeavy tailen_HK
dc.subjectMatuszewska indexen_HK
dc.subjectNegative associationen_HK
dc.subjectPrecise large deviationsen_HK
dc.subjectRandom sumsen_HK
dc.titlePrecise large deviations for sums of random variables with consistently varying tailsen_HK
dc.typeArticleen_HK
dc.identifier.openurlhttp://library.hku.hk:4550/resserv?sid=HKU:IR&issn=0021-9002&volume=41&issue=1&spage=93&epage=107&date=2004&atitle=Precise+large+deviations+for+sums+of+random+variables+with+consistently+varying+tailsen_HK
dc.identifier.emailNg, KW: kaing@hkucc.hku.hken_HK
dc.identifier.emailYang, H: hlyang@hku.hken_HK
dc.identifier.authorityNg, KW=rp00765en_HK
dc.identifier.authorityYang, H=rp00826en_HK
dc.description.naturelink_to_subscribed_fulltext-
dc.identifier.doi10.1239/jap/1077134670en_HK
dc.identifier.scopuseid_2-s2.0-2442459020en_HK
dc.identifier.hkuros85656en_HK
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-2442459020&selection=ref&src=s&origin=recordpageen_HK
dc.identifier.volume41en_HK
dc.identifier.issue1en_HK
dc.identifier.spage93en_HK
dc.identifier.epage107en_HK
dc.identifier.isiWOS:000220186000007-
dc.publisher.placeUnited Kingdomen_HK
dc.identifier.scopusauthoridNg, KW=7403178774en_HK
dc.identifier.scopusauthoridTang, Q=7201632128en_HK
dc.identifier.scopusauthoridYan, JA=7403729432en_HK
dc.identifier.scopusauthoridYang, H=7406559537en_HK

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