Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
10527175 | Stochastic Processes and their Applications | 2015 | 27 Pages |
Abstract
Let {Xi(t),tâ¥0},1â¤iâ¤n be mutually independent centered Gaussian processes with almost surely continuous sample paths. We derive the exact asymptotics of P(âtâ[0,T]âi=1,â¦,nXi(t)>u) as uââ, for both locally stationary Xi's and Xi's with a non-constant generalized variance function. Additionally, we analyze properties of multidimensional counterparts of the Pickands and Piterbarg constants that appear in the derived asymptotics. Important by-products of this contribution are the vector-process extensions of the Piterbarg inequality, the Borell-TIS inequality, the Slepian lemma and the Pickands-Piterbarg lemma which are the main pillars of the extremal theory of vector-valued Gaussian processes.
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
Krzysztof DÈ©bicki, Enkelejd Hashorva, Lanpeng Ji, Kamil TabiÅ,