Portugaliae Mathematica   EMIS ELibM Electronic Journals PORTUGALIAE
Vol. 56, No. 1, pp. 59-72 (1999)

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Maxima and Minima of Stationary Random Sequences under a Local Dependence Restriction

Maria da Graça Temido

Departamento de Matemática, Universidade de Coimbra,
Largo D. Dinis, 3000 Coimbra - PORTUGAL

Abstract: In this paper a local mixing condition $\widetilde D(u_{n},v_{n})$ for stationary random sequences satisfying Davis' condition $D(u_{n},v_{n})$ is introduced. Under these conditions, the asymptotic joint distribution of the maxima and minima can be calculated with the knowledge of the crossing probabilities. An illustrative example of a 2-dependent sequence where the maxima and minima are not asymptotically independent is also given.

Keywords: Nondegenerate limiting distributions; maximum and minimum value; stationary sequence; $m$-dependence.

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Electronic version published on: 31 Jan 2003. This page was last modified: 27 Nov 2007.

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