Limit theorem on the pointwise maxima of minimum of vector-valued Gaussian processes

In this paper, the limit properties of properly time-scaled and normalized maxima of minimum of vector-valued Gaussian processes are studied. It is shown that the maxima of dependent samples of those processes converge weakly on the space of continuous functions to a stochastic process with explicit...

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Bibliographic Details
Published in:Statistics & probability letters 2021-09, Vol.176, p.109137, Article 109137
Main Authors: Tang, Linjun, Zheng, Shengchao, Tan, Zhongquan
Format: Article
Language:English
Subjects:
Brown–Resnick process
Extreme value theory
Functional convergence
The minimum of vector-valued Gaussian processes
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Summary:In this paper, the limit properties of properly time-scaled and normalized maxima of minimum of vector-valued Gaussian processes are studied. It is shown that the maxima of dependent samples of those processes converge weakly on the space of continuous functions to a stochastic process with explicit finite-dimensional distributions.
ISSN:0167-7152
1879-2103
DOI:10.1016/j.spl.2021.109137