Exact asymptotics and limit theorems for supremum of stationary chi-processes over a random interval

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Serval ID
serval:BIB_52769A515A90
Type
Article: article from journal or magazin.
Collection
Publications
Institution
Title
Exact asymptotics and limit theorems for supremum of stationary chi-processes over a random interval
Journal
Stochastic Processes and their Applications
Author(s)
Tan Z., Hashorva E.
ISSN
0304-4149 (Print)
Publication state
Published
Issued date
2013
Peer-reviewed
Oui
Volume
123
Number
8
Pages
2983-2998
Language
english
Abstract
Let {chi(k)(t), t >= 0} be a stationary chi-process with k degrees of freedom being independent of some non-negative random variable T. In this paper we derive the exact asymptotics of P {sup(t is an element of [0, T]) chi(k) (t) > u} as u -> infinity when T has a regularly varying tail with index lambda is an element of [0, 1). Three other novel results of this contribution are the mixed Gumbel limit law of the normalised maximum over an increasing random interval, the Piterbarg inequality and the Seleznjev pth-mean theorem for stationary chi-processes.
Keywords
Chi-process, Limit theorems, Piterbarg inequality, Piterbarg theorem for chi-processes, Seleznjev pth-mean approximation theorem
Web of science
Open Access
Yes
Create date
16/03/2013 17:43
Last modification date
20/08/2019 14:07
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