A local limit theorem for random walk maxima with heavy tails
(2002) In Statistics and Probability Letters 56(4). p.399404 Abstract
 For a random walk with negative mean and heavytailed 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:
http://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
 01677152
 DOI
 10.1016/S01677152(02)000330
 language
 English
 LU publication?
 yes
 id
 856b133a620b4d2ea1adeb6b70c80b14 (old id 340156)
 date added to LUP
 20070802 11:59:07
 date last changed
 20180304 04:31:34
@article{856b133a620b4d2ea1adeb6b70c80b14, abstract = {For a random walk with negative mean and heavytailed 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 = {01677152}, keyword = {integrated tail,ladder height,subexponential distribution}, language = {eng}, number = {4}, pages = {399404}, 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/S01677152(02)000330}, volume = {56}, year = {2002}, }