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A local limit theorem for random walk maxima with heavy tails

Asmussen, Sören LU ; Kalashnikov, V; Konstantinides, D; Kluppelberg, C and Tsitsiashvili, G (2002) In Statistics and Probability Letters 56(4). p.399-404
Abstract
For a random walk with negative mean and heavy-tailed increment distribution F, it is well known that under suitable subexponential assumptions, the distribution pi of the maximum has a tail pi(x, infinity) which is asymptotically proportional to integral(x)(infinity)F(y,infinity) dy. We supplement here this by a local result showing that pi(x, x + z] is asymptotically proportional to zF(x,infinity). (C) 2002 Elsevier Science B.V. All rights reserved.
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
integrated tail, ladder height, subexponential distribution
in
Statistics and Probability Letters
volume
56
issue
4
pages
399 - 404
publisher
Elsevier
external identifiers
  • wos:000175031100007
  • scopus:0037082552
ISSN
0167-7152
DOI
10.1016/S0167-7152(02)00033-0
language
English
LU publication?
yes
id
856b133a-620b-4d2e-a1ad-eb6b70c80b14 (old id 340156)
date added to LUP
2007-08-02 11:59:07
date last changed
2017-01-01 07:19:42
@article{856b133a-620b-4d2e-a1ad-eb6b70c80b14,
  abstract     = {For a random walk with negative mean and heavy-tailed increment distribution F, it is well known that under suitable subexponential assumptions, the distribution pi of the maximum has a tail pi(x, infinity) which is asymptotically proportional to integral(x)(infinity)F(y,infinity) dy. We supplement here this by a local result showing that pi(x, x + z] is asymptotically proportional to zF(x,infinity). (C) 2002 Elsevier Science B.V. All rights reserved.},
  author       = {Asmussen, Sören and Kalashnikov, V and Konstantinides, D and Kluppelberg, C and Tsitsiashvili, G},
  issn         = {0167-7152},
  keyword      = {integrated tail,ladder height,subexponential distribution},
  language     = {eng},
  number       = {4},
  pages        = {399--404},
  publisher    = {Elsevier},
  series       = {Statistics and Probability Letters},
  title        = {A local limit theorem for random walk maxima with heavy tails},
  url          = {http://dx.doi.org/10.1016/S0167-7152(02)00033-0},
  volume       = {56},
  year         = {2002},
}