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Joint Exceedances of High Levels under a Local Dependence Condition

Helena Ferreira
Journal of Applied Probability
Vol. 30, No. 1 (Mar., 1993), pp. 112-120
DOI: 10.2307/3214625
Stable URL: http://www.jstor.org/stable/3214625
Page Count: 9
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Joint Exceedances of High Levels under a Local Dependence Condition
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Abstract

Under appropriate long-range dependence conditions, it is well known that the joint distribution of the number of exceedances of several high levels is asymptotically compound Poisson. Here we investigate the structure of a cluster of exceedances for stationary sequences satisfying a suitable local dependence condition, under which it is only necessary to get certain limiting probabilities, easy to compute, in order to obtain limiting results for the highest order statistics, exceedance counts and upcrossing counts.

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