Extremes of Vector-Valued Gaussian Processes
arXiv:1911.06350
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.
29 pages
References in corpus (3)
- Integral representations and properties of operator fractional Brownian motions
- Maxima of asymptotically Gaussian random fields and moderate deviation approximations to boundary crossing probabilities of sums of random variables with multidimensional indices
- Asymptotics and approximations of ruin probabilities for multivariate risk processes in a Markovian environment