Extreme value theory for multivariate stationary sequences
The author considers multivariate extremal type theorems and some related problems in a setting where the assumptions of independence and linear normalization in the classical setting are weakened. For a stationary sequence of random vectors he introduces a distributional mixing condition which is an obvious extension of \textit{M. R. Leadbetter}'s condition \(D(u_ n)\) in the one-dimensional case [Z. Wahrscheinlichkeitstheorie verw. Gebiete 28, 289-303 (1974; Zbl 0265.60019)]. For a sequence satisfying this condition the following topics are studied. (1) To obtain characterizations of the weak limit F of properly normalized partial maxima. (2) To study a condition under which the partial maxima behave as they would if the sequence were i.i.d. (3) To consider problems in connection with the independence of the margins of F.
scientific article; zbMATH DE number 4113766
scientific article