Mixture results for extremal behaviour of strongly dependent nonstationary Gaussian sequences

• Autores: M. Graça Temido
• Localización: Test: An Official Journal of the Spanish Society of Statistics and Operations Research, ISSN-e 1863-8260, ISSN 1133-0686, Vol. 9, Nº. 2, 2000, págs. 439-453
• Idioma: inglés
• DOI: 10.1007/bf02595744
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• Resumen

  • Let {Xn} be a nonstationary Gaussian sequence. In this work we introduce a condition on rij= Cor(Xi,Xj), i,j >= 1 that models a strong dependence struture. We prove that the limit of the point process of exceedances is a Cox process i.e. a point process whose distribution is a mixture of distributions of simple Poisson processes, regulated by a standard normal law. Moreover, we study the joint limit distribution of the maxima and minima, under linear normalization, and we again find a doubly stochastic behaviour