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"publishedYear" : 2018, "abstractText" : "In this paper we consider the asymptotics of logarithmic tails of a perpetuity R (sic) Sigma(j)=1(infinity) Qj Pi(j-1)(k=1) M-k, where (M-n, Q(n))(n=1)(infinity) are independent and identically distributed copies of (M, Q), for the case when P(M is an element of [0, 1)) = 1 and Q has all exponential moments. If M and Q are independent, under regular variation assumptions, we find the precise asymptotics of - log P(R > x) as x -> infinity. Moreover, we deal with the case of dependent M and Q, and give asymptotic bounds for - log P(R > x). It turns out that the dependence structure between M and Q has a significant impact on the asymptotic rate of logarithmic tails of R. Such a phenomenon is not observed in the case of heavy-tailed perpetuities.", "subjects" : [ { "otype" : "Classification", "mtid" : 10003, "link" : "/api/classification/10003", "label" : "Mathematics", "published" : true, "snippet" : true } ], "keywords" : [ { "otype" : "Keyword", "mtid" : 1103527, "link" : "/api/keyword/1103527", "label" : "regular variation", "published" : true, "oldId" : 1103527, "snippet" : true }, { "otype" : "Keyword", "mtid" : 1547283, "link" : "/api/keyword/1547283", "label" : "Tauberian theorem", "published" : true, "snippet" : true }, { "otype" : "Keyword", "mtid" : 1660071, "link" : "/api/keyword/1660071", "label" : "Perpetuity", "published" : true, "snippet" : true }, { "otype" : "Keyword", "mtid" : 1660072, "link" : "/api/keyword/1660072", "label" : "dependence structure", "published" : true, "snippet" : true }, { "otype" : "Keyword", "mtid" : 1660073, "link" : "/api/keyword/1660073", "label" : "convex conjugate", "published" : true, "snippet" : true } ], "digital" : null, "printed" : null, "sourceYear" : 2019, "foreignEdition" : true, "foreignLanguage" : true, "fullPublication" : true, "conferencePublication" : false, "nationalOrigin" : null, "missingAuthor" : false, "oaType" : "NONE", "oaCheckDate" : "2022-07-29", "oaFree" : false, "citationCount" : 0, "citationCountUnpublished" : 0, "citationCountWoOther" : 0, "independentCitCountWoOther" : 0, "doiCitationCount" : 0, "wosCitationCount" : 0, "scopusCitationCount" : 0, "independentCitationCount" : 0, "unhandledCitationCount" : 0, "citingPubCount" : 0, "independentCitingPubCount" : 0, "unhandledCitingPubCount" : 0, "citedPubCount" : 1, "citedCount" : 1, "ratings" : [ { "otype" : "MtaRating", "mtid" : 507719, "link" : "/api/mtarating/507719", "label" : "IX. 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