### 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 |

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### Keywords

- Random difference equation
- Regular variation
- Subexponential distribution

### Cite this

*Journal of Applied Probability*,

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

}

*Journal of Applied Probability*, vol. 44, no. 4, pp. 1031-1046. https://doi.org/10.1239/jap/1197908822

**On a theorem of Breiman and a class of random difference equations.** / Denisov, Denis; Zwart, Bert.

Research output: Contribution to journal › Article

TY - JOUR

T1 - On a theorem of Breiman and a class of random difference equations

AU - Denisov, Denis

AU - Zwart, Bert

PY - 2007/12

Y1 - 2007/12

N2 - 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{Ya+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.

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 a and that E{Ya+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.

KW - Random difference equation

KW - Regular variation

KW - Subexponential distribution

UR - http://www.scopus.com/inward/record.url?scp=38949137348&partnerID=8YFLogxK

U2 - 10.1239/jap/1197908822

DO - 10.1239/jap/1197908822

M3 - Article

VL - 44

SP - 1031

EP - 1046

JO - Journal of Applied Probability

JF - Journal of Applied Probability

SN - 0021-9002

IS - 4

ER -