Extremes of vector-valued Gaussian processes: exact asymptotics

By Krzysztof Dcebicki, Enkelejd Hashorva, Lanpeng Ji, Kamil Tabi's. 2015

56 citations recorded by the source corpus.

Let {Xi(t),t≥0},1≤i≤n be mutually independent centered Gaussian processes with almost surely continuous sample paths. We derive the exact asymptotics of P(∃t∈[0,T]∀i=1,…,nXi(t)>u) as u→∞, 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.

Subfields: Finance, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/01f85f8b70cad91a80614417ef003984eac356a9

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Finance

1. Enkelejd Hashorva
2. Sebastian Engelke
3. Krzysztof Debicki

In Management Science and Operations Research

1. Enkelejd Hashorva
2. Sebastian Engelke

Citations in the corpus

• Generalized Pickands constants and stationary max-stable processes (2016, background): “holds under some mild regularity conditions on the correlation and the variance function ofX (Pickands, 1969; Berman, 1982, 1992; Piterbarg, 1996, 2015; Dȩbicki et al., 2015).”