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Perpetuities with thin tails

Part of: Distribution theory - Probability Stochastic analysis

Published online by Cambridge University Press:  01 July 2016

Charles M. Goldie  and
Rudolf Grübel
Charles M. Goldie
Affiliation:
Queen Mary and Westfield College, University of London
Rudolf Grübel*
Affiliation:
Universität Hannover
*
∗∗ Postal address: Institut für Mathematische Stochastik, Universität Hannover, Postfach 6009, 30060 Hannover, Germany.
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Abstract

We investigate the behaviour of P(R ≧ r) and P(R ≦ −r) as r → ∞for the random variable where is an independent, identically distributed sequence with P(− 1 ≦ M ≦ 1) = 1. Random variables of this type appear in insurance mathematics, as solutions of stochastic difference equations, in the analysis of probabilistic algorithms and elsewhere. Exponential and Poissonian tail behaviour can arise.

Keywords

PERPETUITYRANDOM AFFINE MAPSELECTION ALGORITHMSTOCHASTIC DIFFERENCE EQUATIONSTOCHASTIC DISCOUNTINGTAIL BEHAVIOUR

MSC classification

Primary: 60H25: Random operators and equations 60E99: None of the above, but in this section
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 28 , Issue 2 , June 1996 , pp. 463 - 480
Copyright
Copyright © Applied Probability Trust 1996 

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Footnotes

∗

Present address: School of Mathematical Sciences, University of Sussex, Brighton, BN1 9QH, UK.

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