### Abstract

We study distributions F on [0, 8) such that for some T = 8, F*^{2}(x, x+T] ~ 2F(x, x+T]. The case T = 8 corresponds to F being subexponential, and our analysis shows that the properties for T < 8 are, in fact, very similar to this classical case. A parallel theory is developed in the presence of densities. Applications are given to random walks, the key renewal theorem, compound Poisson process and Bellman-Harris branching processes.

Original language | English |
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Pages (from-to) | 489-518 |

Number of pages | 30 |

Journal | Journal of Theoretical Probability |

Volume | 16 |

Issue number | 2 |

DOIs | |

Publication status | Published - Apr 2003 |

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### Keywords

- Distribution tails
- Local probabilities
- Subexponential distributions
- Sums of independent random variables

### Cite this

*Journal of Theoretical Probability*,

*16*(2), 489-518. https://doi.org/10.1023/A:1023535030388

}

*Journal of Theoretical Probability*, vol. 16, no. 2, pp. 489-518. https://doi.org/10.1023/A:1023535030388

**Asymptotics for Sums of Random Variables with Local Subexponential Behaviour.** / Asmussen, Søren; Foss, Serguei; Korshunov, Dmitry.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Asymptotics for Sums of Random Variables with Local Subexponential Behaviour

AU - Asmussen, Søren

AU - Foss, Serguei

AU - Korshunov, Dmitry

PY - 2003/4

Y1 - 2003/4

N2 - We study distributions F on [0, 8) such that for some T = 8, F*2(x, x+T] ~ 2F(x, x+T]. The case T = 8 corresponds to F being subexponential, and our analysis shows that the properties for T < 8 are, in fact, very similar to this classical case. A parallel theory is developed in the presence of densities. Applications are given to random walks, the key renewal theorem, compound Poisson process and Bellman-Harris branching processes.

AB - We study distributions F on [0, 8) such that for some T = 8, F*2(x, x+T] ~ 2F(x, x+T]. The case T = 8 corresponds to F being subexponential, and our analysis shows that the properties for T < 8 are, in fact, very similar to this classical case. A parallel theory is developed in the presence of densities. Applications are given to random walks, the key renewal theorem, compound Poisson process and Bellman-Harris branching processes.

KW - Distribution tails

KW - Local probabilities

KW - Subexponential distributions

KW - Sums of independent random variables

UR - http://www.scopus.com/inward/record.url?scp=0037689168&partnerID=8YFLogxK

U2 - 10.1023/A:1023535030388

DO - 10.1023/A:1023535030388

M3 - Article

VL - 16

SP - 489

EP - 518

JO - Journal of Theoretical Probability

JF - Journal of Theoretical Probability

SN - 0894-9840

IS - 2

ER -