On limiting cluster size distributions for processes of exceedances for stationary sequences

2010/04/28 by Borovkov, Konstantin, Novak, Serguei
#60G70 #60J05 #60K05 #60K15 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1004.4955

Abstract

It is well known that, under broad assumptions, the time-scaled point process of exceedances of a high level by a stationary sequence converges to a compound Poisson process as the level grows. The purpose of this note is to demonstrate that, for any given distribution G on the natural numbers, there exists a stationary sequence for which the compounding law of this limiting process of exceedances will coincide with G.

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