%0 Journal Article
%T Perpetuities with thin tails revisited
%A Pawe£¿ Hitczenko
%A Jacek Weso£¿owski
%J Mathematics
%D 2009
%I arXiv
%R 10.1214/09-AAP603
%X We consider the tail behavior of random variables $R$ which are solutions of the distributional equation $R\stackrel{d}{=}Q+MR$, where $(Q,M)$ is independent of $R$ and $|M|\le 1$. Goldie and Gr\"{u}bel showed that the tails of $R$ are no heavier than exponential and that if $Q$ is bounded and $M$ resembles near 1 the uniform distribution, then the tails of $R$ are Poissonian. In this paper, we further investigate the connection between the tails of $R$ and the behavior of $M$ near 1. We focus on the special case when $Q$ is constant and $M$ is nonnegative.
%U http://arxiv.org/abs/0912.1694v3