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

Maria da Graça Temido

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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