Extremes of Vector-Valued Gaussian Processes

Autor:	Dȩbicki, Krzysztof, Hashorva, Enkelejd, Wang, Longmin
Rok vydání:	2019
Předmět:	Mathematics - Probability Primary 60G15 secondary 60G70
Druh dokumentu:	Working Paper
Popis:	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. Comment: 29 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1911.06350 Zobrazit plný text záznamu View this record from Arxiv