Extremes of Vector-Valued Gaussian Processes

Krzysztof Dȩbicki; Enkelejd Hashorva; Longmin Wang

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arXiv · 1911.06350

Extremes of Vector-Valued Gaussian Processes

Krzysztof Dȩbicki·Enkelejd Hashorva·Longmin Wang

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Abstract

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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Krzysztof Dȩbicki, Enkelejd Hashorva, Longmin Wang. 2019-11-14. Extremes of Vector-Valued Gaussian Processes. https://arxiv.org/abs/1911.06350

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