On perpetuities with light tails

• Published in: Advances in applied probability Vol. 50; no. 4; pp. 1119 - 1154
• Main Author: Kołodziejek, Bartosz
• Format: Journal Article
• Language: English
• Published: Cambridge, UK Cambridge University Press 01.12.2018; Applied Probability Trust
• Subjects: Asymptotic properties; Dependence; Original Article; Probability; convex conjugate; Tauberian theorem; Primary 60H25; Secondary 60E99; dependence structure; Perpetuity; regular variation

In this paper we consider the asymptotics of logarithmic tails of a perpetuity R=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 and Q has all exponential moments. If M and Q are independent, under regular variation ass...