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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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

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

First available in Project Euclid: 17 December 2007

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

Regular variation subexponential distribution random difference equation


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.

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