A local limit theorem for random walk maxima with heavy tails

被引：61

作者：

Asmussen, S

Kalashnikov, V

Konstantinides, D

Klüppelberg, C

Tsitsiashvili, G

机构：

[1] Lund Univ, Dept Math Stat, S-22100 Lund, Sweden

[2] Univ Copenhagen, Dept Actuarial Math, DK-2100 Copenhagen, Denmark

[3] Univ Aegean, Dept Math, Samos 83200, Greece

[4] Tech Univ Munich, Ctr Math Sci, D-80290 Munich, Germany

[5] Russian Acad Sci, Inst Appl Math, Vladivostok 690041, Russia

来源：

STATISTICS & PROBABILITY LETTERS | 2002年 / 56卷 / 04期

关键词：

integrated tail; ladder height; subexponential distribution;

D O I：

10.1016/S0167-7152(02)00033-0

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

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.

引用

页码：399 / 404

页数：6

共 11 条

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Asmussen S, 1998, ANN APPL PROBAB, V8, P354

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