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

89 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

Access to Document

10.1023/A:1023535030388

Cite this

@article{a06610dc814847f29319c37526cc286f,

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] ~ 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.",

keywords = "Distribution tails, Local probabilities, Subexponential distributions, Sums of independent random variables",

author = "S{\o}ren Asmussen and Serguei Foss and Dmitry Korshunov",

year = "2003",

month = apr,

doi = "10.1023/A:1023535030388",

language = "English",

volume = "16",

pages = "489--518",

journal = "Journal of Theoretical Probability",

issn = "1572-9230",

publisher = "Springer",

number = "2",

}

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

SN - 1572-9230

VL - 16

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

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this