2012/05/31 by Sebastian Engelke, Zakhar Kabluchko, Martin Schlather · 10 citations
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #Bivariate analysis #Class (philosophy) #Financial Risk and Volatility Modeling #Function (biology) #Gaussian #Gaussian process #Maxima #Measure (data warehouse) #Monotone polygon #Probability and Risk Models #Random variable #Set (abstract data type) #Statistical Methods and Inference #math.PR #math.ST #stat.TH
paper · pdf · doi:10.3150/13-bej560
published in Bernoulli 21(1) (Chapman and Hall London) · Published at http://dx.doi.org/10.3150/13-BEJ560 in the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm)
openalex publication_date 2015/02/01 · arxiv created 2015/04/07 · arxiv updated 2015/04/08 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
Let Xi,n, n∈ℕ, 1≤ i≤ n, be a triangular array of independent ℝd-valued Gaussian random vectors with correlation matrices Σi,n. We give necessary conditions under which the row-wise maxima converge to some max-stable distribution which generalizes the class of Hüsler–Reiss distributions. In the bivariate case, the conditions will also be sufficient. Using these results, new models for bivariate extremes are derived explicitly. Moreover, we define a new class of stationary, max-stable processes as max-mixtures of Brown–Resnick processes. As an application, we show that these processes realize a large set of extremal correlation functions, a natural dependence measure for max-stable processes. This set includes all functions ψ(√(γ(h))), h∈ℝd, where ψ is a completely monotone function and γ is an arbitrary variogram.