On the probability of conjunctions of stationary Gaussian processes

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Serval ID
serval:BIB_8591F77E59C3
Type
Article: article from journal or magazin.
Collection
Publications
Institution
Title
On the probability of conjunctions of stationary Gaussian processes
Journal
Statistics & Probability Letters
Author(s)
Dȩbicki K., Hashorva E., Ji L., Tabiś K.
ISSN
0167-7152 (Print)
Publication state
Published
Issued date
2014
Peer-reviewed
Oui
Volume
88
Pages
141-148
Language
english
Abstract
Let {X-i(t), t >= 0}, 1 <= i <= n be independent centered stationary Gaussian processes with unit variance and almost surely continuous sample paths. For given positive constants u, T, define the set of conjunctions C-[0,C-T],C-u := {t is an element of [0, T] : min(1 <= i <= n) X-i(t) >= u}. Motivated by some applications in brain mapping and digital communication systems, we obtain exact asymptotic expansion of P {C-[0,C-T],C-u not equal phi}, as u -> infinity. Moreover, we establish the Berman sojourn limit theorem for the random process [min(1 <=iota <= n) X-i(t), t >= 0) and derive the tail asymptotics of the supremum of each order statistics process.
Keywords
Stationary Gaussian processes, Order statistics processes, Conjunction, Extremes, Berman sojourn limit theorem, Generalized Pickands constant
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03/02/2014 20:59
Last modification date
20/08/2019 14:44
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