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Asymptotics for sums of random variables with local subexponential behaviour

Asmussen, Sören LU ; Foss, S and Korshunov, D (2003) In Journal of Theoretical Probability 16(2). p.489-518
Abstract
We study distributions F on [0, infinity) such that for some T less than or equal to infinity F*(2)(x, x + T] similar to 2F(x, x + T]. The case T = infinity corresponds to F being subexponential, and our analysis shows that the properties for T < &INFIN; 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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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
local probabilities, distribution tails, Sums of independent random variables, subexponential distributions
in
Journal of Theoretical Probability
volume
16
issue
2
pages
489 - 518
publisher
Kluwer
external identifiers
  • wos:000182480800013
  • scopus:0037689168
ISSN
1572-9230
DOI
10.1023/A:1023535030388
language
English
LU publication?
yes
id
391728fc-257f-4a5e-9235-b2ba345b8d83 (old id 312684)
date added to LUP
2007-08-02 11:21:13
date last changed
2018-08-05 04:05:32
@article{391728fc-257f-4a5e-9235-b2ba345b8d83,
  abstract     = {We study distributions F on [0, infinity) such that for some T less than or equal to infinity F*(2)(x, x + T] similar to 2F(x, x + T]. The case T = infinity corresponds to F being subexponential, and our analysis shows that the properties for T &lt; &amp;INFIN; 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.},
  author       = {Asmussen, Sören and Foss, S and Korshunov, D},
  issn         = {1572-9230},
  keyword      = {local probabilities,distribution tails,Sums of independent random variables,subexponential distributions},
  language     = {eng},
  number       = {2},
  pages        = {489--518},
  publisher    = {Kluwer},
  series       = {Journal of Theoretical Probability},
  title        = {Asymptotics for sums of random variables with local subexponential behaviour},
  url          = {http://dx.doi.org/10.1023/A:1023535030388},
  volume       = {16},
  year         = {2003},
}