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

Denis Denisov; Bert Zwart

doi:10.1239/jap/1197908822

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

Denis Denisov, Bert Zwart

Research output: Contribution to journal › Article › peer-review

44 Citations (Scopus)

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 a and that E{Y^a+e] < 8 for some e > 0. We investigate when the condition on Y can be weakened and apply our findings to analyze a class of random difference equations. © Applied Probability Trust 2007.

Original language	English
Pages (from-to)	1031-1046
Number of pages	16
Journal	Journal of Applied Probability
Volume	44
Issue number	4
DOIs	https://doi.org/10.1239/jap/1197908822
Publication status	Published - Dec 2007

Keywords

Random difference equation
Regular variation
Subexponential distribution

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10.1239/jap/1197908822

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

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Keywords

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