Exact tail asymptotics of the supremum of strongly dependent gaussian processes over a random interval

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Type
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Publications
Institution
Title
Exact tail asymptotics of the supremum of strongly dependent gaussian processes over a random interval
Journal
Lithuanian Mathematical Journal
Author(s)
Tan Z., Hashorva E.
ISSN
0363-1672
Publication state
Published
Issued date
03/2013
Peer-reviewed
Oui
Volume
53
Number
1
Pages
91-102
Language
english
Abstract
Let be a positive random variable independent of a real-valued stochastic process . In this paper, we investigate the asymptotic behavior of as u -> a assuming that X is a strongly dependent stationary Gaussian process and has a regularly varying survival function at infinity with index lambda a [0, 1). Under asymptotic restrictions on the correlation function of the process, we show that with some positive finite constant c and function m(center dot) defined in terms of the local behavior of the correlation function and the standard Gaussian distribution.
Keywords
Gaussian processes, Strong dependence, Supremum over a random interval, Exact tail asymptotics, Pickands constant
Web of science
Open Access
Yes
Create date
24/10/2012 14:29
Last modification date
20/08/2019 15:29
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