### 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 |
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Pages (from-to) | 1031-1046 |

Number of pages | 16 |

Journal | Journal of Applied Probability |

Volume | 44 |

Issue number | 4 |

DOIs | |

Publication status | Published - Dec 2007 |

### Keywords

- Random difference equation
- Regular variation
- Subexponential distribution

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## Cite this

Denisov, D., & Zwart, B. (2007). On a theorem of Breiman and a class of random difference equations.

*Journal of Applied Probability*,*44*(4), 1031-1046. https://doi.org/10.1239/jap/1197908822