### Abstract

For a distribution F^{*t} of a random sum S_{t} = ?_{1} + ... + ?_{t} of i.i.d, random variables with a common distribution F on the half-line [0, 8), we study the limits of the ratios of tails F^{*t} (x)/F (x) as x ? 8 (here, t is a counting random variable which does not depend on {? _{n}}_{n}= 1). We also consider applications of the results obtained to random walks, compound Poisson distributions, infinitely divisible laws, and subcritical branching processes. © 2008 ISI/BS.

Original language | English |
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Pages (from-to) | 391-404 |

Number of pages | 14 |

Journal | Bernoulli |

Volume | 14 |

Issue number | 2 |

DOIs | |

Publication status | Published - May 2008 |

### Keywords

- Convolution equivalence
- Convolution tail
- Lower limit
- Randomly stopped sums
- Subexponential distribution

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## Cite this

Denisov, D., Foss, S., & Korshunov, D. (2008). On lower limits and equivalences for distribution tails of randomly stopped sums.

*Bernoulli*,*14*(2), 391-404. https://doi.org/10.3150/07-BEJ111