Asymptotics for sums of random variables with local subexponential behaviour
(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.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/312684
- author
- Asmussen, Sören LU ; Foss, S and Korshunov, D
- organization
- publishing date
- 2003
- 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
- Springer
- 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
- 2016-04-01 15:49:01
- date last changed
- 2022-04-15 00:07:14
@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 < &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}}, keywords = {{local probabilities; distribution tails; Sums of independent random variables; subexponential distributions}}, language = {{eng}}, number = {{2}}, pages = {{489--518}}, publisher = {{Springer}}, 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}}, doi = {{10.1023/A:1023535030388}}, volume = {{16}}, year = {{2003}}, }