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December 2009 Perpetuities with thin tails revisited
Paweł Hitczenko, Jacek Wesołowski
Ann. Appl. Probab. 19(6): 2080-2101 (December 2009). DOI: 10.1214/09-AAP603

Abstract

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|≤1. Goldie and Grübel 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.

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Paweł Hitczenko. Jacek Wesołowski. "Perpetuities with thin tails revisited." Ann. Appl. Probab. 19 (6) 2080 - 2101, December 2009. https://doi.org/10.1214/09-AAP603

Information

Published: December 2009
First available in Project Euclid: 25 November 2009

zbMATH: 1185.60074
MathSciNet: MR2588240
Digital Object Identifier: 10.1214/09-AAP603

Subjects:
Primary: 60H25
Secondary: 60E99

Rights: Copyright © 2009 Institute of Mathematical Statistics

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Vol.19 • No. 6 • December 2009
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