The Annals of Applied Probability

Perpetuities with thin tails revisited

Paweł Hitczenko and Jacek Wesołowski

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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.

Article information

Source
Ann. Appl. Probab., Volume 19, Number 6 (2009), 2080-2101.

Dates
First available in Project Euclid: 25 November 2009

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1259158767

Digital Object Identifier
doi:10.1214/09-AAP603

Mathematical Reviews number (MathSciNet)
MR2588240

Zentralblatt MATH identifier
1185.60074

Subjects
Primary: 60H25: Random operators and equations [See also 47B80]
Secondary: 60E99: None of the above, but in this section

Keywords
Perpetuity stochastic difference equation tail behavior

Citation

Hitczenko, Paweł; Wesołowski, Jacek. Perpetuities with thin tails revisited. Ann. Appl. Probab. 19 (2009), no. 6, 2080--2101. doi:10.1214/09-AAP603. https://projecteuclid.org/euclid.aoap/1259158767


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References

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