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On the Maximum Exceedance of a Sequence of Random Variables Over a Renewal Threshold

Part of: Stochastic processes

Published online by Cambridge University Press:  14 July 2016

Xuemiao Ha ,
Qihe Tang  and
Li Wei
Xuemiao Ha*
Affiliation:
The University of Iowa
Qihe Tang*
Affiliation:
The University of Iowa
Li Wei*
Affiliation:
Renmin University of China
*
∗Postal address: Department of Statistics and Actuarial Science, The University of Iowa, 241 Schaeffer Hall, Iowa City, IA 52242, USA.
∗Postal address: Department of Statistics and Actuarial Science, The University of Iowa, 241 Schaeffer Hall, Iowa City, IA 52242, USA.
∗∗∗∗Postal address: School of Finance, Renmin University of China, Beijing, 100872, P. R. China. Email address: weil@ruc.edu.cn
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Abstract

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In this paper we study the tail behavior of the maximum exceedance of a sequence of independent and identically distributed random variables over a random walk. For both light-tailed and heavy-tailed cases, we derive a precise asymptotic formula, which extends and unifies some existing results in the recent literature of applied probability.

Keywords

Asymptoticsexceedancerandom walktail probabilitythe classes (γ) and (γ)

MSC classification

Secondary: 60G50: Sums of independent random variables; random walks 60G70: Extreme value theory; extremal processes
Type
Research Article
Information
Journal of Applied Probability , Volume 46 , Issue 2 , June 2009 , pp. 559 - 570
Copyright
Copyright © Applied Probability Trust 2009 

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