Piterbarg's max-discretization theorem for stationary vector Gaussian processes observed on different grids

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Type
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Publications
Institution
Title
Piterbarg's max-discretization theorem for stationary vector Gaussian processes observed on different grids
Journal
Statistics
Author(s)
Hashorva  E., Tan  Z.
ISSN
0233-1888 (Print)
1029-4910 (Electronic)
Publication state
Published
Issued date
03/2015
Peer-reviewed
Oui
Volume
49
Number
2
Pages
338-360
Language
english
Abstract
In this paper, we derive Piterbarg's max-discretization theorem for two different grids considering centred stationary vector Gaussian processes. So far in the literature results in this direction have been derived for the joint distribution of the maximum of Gaussian processes over and over a grid . In this paper, we extend the recent findings by considering additionally the maximum over another grid . We derive the joint limiting distribution of maximum of stationary Gaussian vector processes for different choices of such grids by letting . As a by-product we find that the joint limiting distribution of the maximum over different grids, which we refer to as the Piterbarg distribution, is in the case of weakly dependent Gaussian processes a max-stable distribution.
Keywords
extremes of Gaussian processes, Piterbarg distribution, Berman condition, limiting distribution, Gumbel limit law, Pickands constant, Piterbarg's max-discretization theorem
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Create date
21/10/2014 20:19
Last modification date
21/08/2019 6:09
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