A local limit theorem for random walk maxima with heavy tails
(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.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/340156
- author
- Asmussen, Sören LU ; Kalashnikov, V ; Konstantinides, D ; Kluppelberg, C and Tsitsiashvili, G
- organization
- publishing date
- 2002
- 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
- 2016-04-01 16:57:14
- date last changed
- 2022-01-28 23:17:31
@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}}, keywords = {{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}}, doi = {{10.1016/S0167-7152(02)00033-0}}, volume = {{56}}, year = {{2002}}, }