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

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 ?? and that E\{Y??+??\} {\textless} ??? for some ?? {\textgreater} 0. We investigate when the condition on Y can be weakened and apply our findings to analyze a class of random difference equations.

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

subexponential distribution

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http://projecteuclid.org/euclid.jap/1197908822

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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 ?? and that E\textbackslash{}\{Y??+??\textbackslash{}\} \{\textbackslash{}textless\} ??? for some ?? \{\textbackslash{}textgreater\} 0. We investigate when the condition on Y can be weakened and apply our findings to analyze a class of random difference equations.",

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AU - Zwart, Bert

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AB - 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 ?? and that E\{Y??+??\} {\textless} ??? for some ?? {\textgreater} 0. We investigate when the condition on Y can be weakened and apply our findings to analyze a class of random difference equations.

KW - subexponential distribution

U2 - 10.1239/jap/1197908822

DO - 10.1239/jap/1197908822

M3 - Article

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SP - 1031

EP - 1046

JO - Journal of Applied Probability

JF - Journal of Applied Probability

IS - 4

ER -

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

Abstract

Keywords

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