Ji, L orcid.org/0000-0002-7790-7765 and Peng, X (2023) Extreme value theory for a sequence of suprema of a class of Gaussian processes with trend. Stochastic Processes and their Applications, 158. pp. 418-452. ISSN 0304-4149
Abstract
We investigate extreme value theory of a class of random sequences defined by the all-time suprema of aggregated self-similar Gaussian processes with trend. This study is motivated by its potential applications in various areas and its theoretical interestingness. We consider both stationary sequences and non-stationary sequences obtained by considering whether the trend functions are identical or not. We show that a sequence of suitably normalised
th order statistics converges in distribution to a limiting random variable which can be a negative log transformed Erlang distributed random variable, a Normal random variable or a mixture of them, according to three conditions deduced through the model parameters. Remarkably, this phenomenon resembles that for the stationary Normal sequence. We also show that various moments of the normalised
th order statistics converge to the moments of the corresponding limiting random variable. The obtained results enable us to analyze various properties of these random sequences, which reveals the interesting particularities of this class of random sequences in extreme value theory.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2023 Published by Elsevier B.V. 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. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/. |
Keywords: | Extreme value; self-similarity; Gaussian processes; fractional Brownian motion; generalized Weibull-like distribution; moments; Pickands constant; Poisson convergence; order statistics; phantom distribution function; extremal index |
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: | 13 Feb 2023 16:25 |
Last Modified: | 24 Jan 2024 01:13 |
Status: | Published |
Publisher: | Elsevier |
Identification Number: | 10.1016/j.spa.2023.01.013 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:195596 |