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Remarks on the absolute maximum of a Lévy process

Part of: Limit theorems Stochastic processes

Published online by Cambridge University Press:  14 July 2016

Mykola Bratiychuk
Mykola Bratiychuk*
Affiliation:
Silesian Technical University
*
∗ Postal address: Instytut Matematyki, Kaszubska st. 23, 44-100 Gliwice, Poland. Email address: bratiich@zeus.polsl.gliwice.pl
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Abstract

Asymptotic behaviour of the distribution of the absolute maximum of a process with independent increments is studied depending on the properties of the Lévy measure of the process. Some applications to the risk process are also considered.

Keywords

Lévy processslowly oscillating functionrisk process

MSC classification

Primary: 60G50: Sums of independent random variables; random walks
Secondary: 60F99: None of the above, but in this section
Type
Research Papers
Information
Journal of Applied Probability , Volume 39 , Issue 2 , June 2002 , pp. 282 - 295
Copyright
Copyright © Applied Probability Trust 2002 

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