# On the probability of conjunctions of stationary Gaussian processes

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State: Serval

Version: author

State: Serval

Version: author

Serval ID

serval:BIB_8591F77E59C3

Type

**Article**: article from journal or magazin.

Collection

Publications

Fund

Title

On the probability of conjunctions of stationary Gaussian processes

Journal

Statistics & Probability Letters

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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Create date

03/02/2014 21:59

Last modification date

03/03/2018 18:57