Journal of Applied Probability

On a theorem of Breiman and a class of random difference equations

Denis Denisov and Bert Zwart

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Abstract

We consider the tail behavior of the product of two independent nonnegative random variables X and Y. Breiman (1965) has considered this problem, assuming that X is regularly varying with index α and that E{Yα+ε} < ∞ for some ε > 0. We investigate when the condition on Y can be weakened and apply our findings to analyze a class of random difference equations.

Article information

Source
J. Appl. Probab. Volume 44, Number 4 (2007), 1031-1046.

Dates
First available in Project Euclid: 17 December 2007

Permanent link to this document
https://projecteuclid.org/euclid.jap/1197908822

Digital Object Identifier
doi:10.1239/jap/1197908822

Mathematical Reviews number (MathSciNet)
MR2382943

Zentralblatt MATH identifier
1141.60041

Subjects
Primary: 60H25: Random operators and equations [See also 47B80] 60J30 60F10: Large deviations

Keywords
Regular variation subexponential distribution random difference equation

Citation

Denisov, Denis; Zwart, Bert. On a theorem of Breiman and a class of random difference equations. J. Appl. Probab. 44 (2007), no. 4, 1031--1046. doi:10.1239/jap/1197908822. https://projecteuclid.org/euclid.jap/1197908822


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