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Joint Exceedances of High Levels under a Local Dependence Condition
Journal of Applied Probability
Vol. 30, No. 1 (Mar., 1993), pp. 112-120
Published by: Applied Probability Trust
Stable URL: http://www.jstor.org/stable/3214625
Page Count: 9
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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.
Journal of Applied Probability © 1993 Applied Probability Trust