### Abstract

For a distribution F*t of a random sum St=¿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 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.

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

Journal | Bernoulli |

Volume | 14 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2008 |

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## Cite this

Denisov, D. E., Foss, S. G., & Korshunov, D. A. (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