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Asymptotically (in)dependent multivariate maxima of moving maxima process. (English) Zbl 1150.60030
A multivariate maximum of the moving maxima model (and some generalizations) of the form \[ Y_{i,d}=\max_i\max_k a_{l,k,d} W_{l,i-k} \] is considered, where \(a_{l,k,d}\) are some nonrandom coefficients, \(W_{l,i}\) are i.i.d. with generalized extreme value distribution. The authors derive formulas for the asymptotic dependency index \[ \lambda_{d,d'}=\lim_{x\to\infty} P(Y_{i,d}>x| Y_{i,d'}>x) \] (asymptotic independence corresponds to \(\lambda_{d,d'}=0\)) and for the extremal index of \(Y_{i,d}\). Results of simulations are presented.

MSC:
60G70 Extreme value theory; extremal stochastic processes
62H05 Characterization and structure theory for multivariate probability distributions; copulas
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