On perpetuities with light tails
Copyright policy )On perpetuities with light tails
AbstractIn this paper we consider the asymptotics of logarithmic tails of a perpetuityR=D∑j=1∞Qj∏k=1j-1Mk, where (Mn,Qn)n=1∞are independent and identically distributed copies of (M,Q), for the case when ℙ(M∈[0,1))=1 andQhas all exponential moments. IfMandQare independent, under regular variation assumptions, we find the precise asymptotics of -logℙ(R>x) asx→∞. Moreover, we deal with the case of dependentMandQ, and give asymptotic bounds for -logℙ(R>x). It turns out that the dependence structure betweenMandQhas a significant impact on the asymptotic rate of logarithmic tails ofR. Such a phenomenon is not observed in the case of heavy-tailed perpetuities.
Primary 60H25, Secondary 60E99, Sums of independent random variables; random walks, Probability (math.PR), Random operators and equations (aspects of stochastic analysis), perpetuity, Tauberian theorem, Distribution theory, FOS: Mathematics, regular variation, convex conjugate, dependence structure, Probability
Primary 60H25, Secondary 60E99, Sums of independent random variables; random walks, Probability (math.PR), Random operators and equations (aspects of stochastic analysis), perpetuity, Tauberian theorem, Distribution theory, FOS: Mathematics, regular variation, convex conjugate, dependence structure, Probability
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).4 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Average influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Average impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!