Extremes of vector-valued Gaussian processes

Krzysztof Dȩbicki, Enkelejd Hashorva and Longmin Wang

Stochastic Processes and their Applications, 2020, vol. 130, issue 9, 5802-5837

Abstract: The seminal papers of Pickands (Pickands, 1967; Pickands, 1969) 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, 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 high exceedance probabilities for both stationary and n on-stationary Gaussian processes. We apply our findings to the operator fractional Brownian motion and Ornstein–Uhlenbeck process.

Keywords: High exceedance probability; Vector-valued Gaussian process; Operator fractional Ornstein–Uhlenbeck processes; Operator fractional Brownian motion; Uniform double-sum method; Vector-valued Borell-TIS inequality (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (1)

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DOI: 10.1016/j.spa.2020.04.008

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