Dȩbicki, K, Hashorva, E, Ji, L orcid.org/0000-0002-7790-7765 et al. (1 more author) (2015) Extremes of vector-valued Gaussian processes: Exact asymptotics. Stochastic Processes and their Applications, 125 (11). pp. 4039-4065. ISSN 0304-4149
Abstract
Let {Xi (t), t ≥ 0}, 1 ≤ i ≤ n be mutually independent centered Gaussian processes with almost surely continuous sample paths. We derive the exact asymptotics of
P (∃t∈[0,T ]∀i=1,...,n Xi(t) > )
as u → ∞, for both locally stationary Xi’s and Xi’s with a non-constant generalized variance function. Additionally, we analyze properties of multidimensional counterparts of the Pickands and Piterbarg constants that appear in the derived asymptotics. Important by-products of this contribution are the vector-process extensions of the Piterbarg inequality, the Borell–TIS inequality, the Slepian lemma and the Pickands–Piterbarg lemma which are the main pillars of the extremal theory of vector-valued Gaussian processes.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2015, Elsevier B.V. All rights reserved. This is an author produced version of an article published in Stochastic Processes and their Applications. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Gaussian process; Conjunction; Extremes; Double-sum method; Slepian lemma; Borell–TIS inequality; Piterbarg inequality; Generalized Pickands constant; Generalized Piterbarg constant; Pickands–Piterbarg lemma |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Statistics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 26 Jun 2019 14:13 |
Last Modified: | 26 Jun 2019 14:13 |
Status: | Published |
Publisher: | Elsevier |
Identification Number: | 10.1016/j.spa.2015.05.015 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:147171 |