Asymptotics for Sums of Random Variables with Local Subexponential Behaviour

Søren Asmussen; Serguei Foss; Dmitry Korshunov

doi:10.1023/A:1023535030388

Asymptotics for Sums of Random Variables with Local Subexponential Behaviour

Søren Asmussen
, Serguei Foss
, Dmitry Korshunov

Research output: Contribution to journal › Article › peer-review

94 Citations (Scopus)

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
Pages (from-to)	489-518
Number of pages	30
Journal	Journal of Theoretical Probability
Volume	16
Issue number	2
DOIs	https://doi.org/10.1023/A:1023535030388
Publication status	Published - Apr 2003

Keywords

Distribution tails
Local probabilities
Subexponential distributions
Sums of independent random variables

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title = "Asymptotics for Sums of Random Variables with Local Subexponential Behaviour",

abstract = "We study distributions F on [0, 8) such that for some T = 8, F*2(x, x+T] \textasciitilde{} 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.",

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AU - Asmussen, Søren

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AU - Korshunov, Dmitry

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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 - https://www.scopus.com/pages/publications/0037689168

U2 - 10.1023/A:1023535030388

DO - 10.1023/A:1023535030388

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SP - 489

EP - 518

JO - Journal of Theoretical Probability

JF - Journal of Theoretical Probability

IS - 2

ER -

Asymptotics for Sums of Random Variables with Local Subexponential Behaviour

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Keywords

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