Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Extremes of Vector-Valued Gaussian Processes   The seminal papers of Pickands [1,2] paved the way for a systematic study of
high exceedance probabilities of both stationary and non-stationary Gaussian
processes. Yet, in the vector-valued setting, due to the lack of key tools
including Slepian's Lemma, Borell-TIS and Piterbarg inequalities there has not
been any methodological development in the literature for the study of extremes
of vector-valued Gaussian processes. In this contribution we develop the
uniform double-sum method for the vector-valued setting obtaining the exact
asymptotics of the exceedance probabilities for both stationary and
non-stationary Gaussian processes. We apply our findings to the operator
fractional Brownian motion and the operator fractional Ornstein-Uhlenbeck
process.

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The categories of this paper are: patt-sol
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The categories of this paper are: plasm-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-lat
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The categories of this paper are: atom-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: chem-ph
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The categories of this paper are: funct-an
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The categories of this paper are: q-alg
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The categories of this paper are: quant-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-fin
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The categories of this paper are: chao-dyn
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The categories of this paper are: bayes-an
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The categories of this paper are: physics