Extremes of Moving Averages of Random Variables from the Domain of Attraction of the Double Exponential Distribution

摘要

This document studies the extreme value behavior of a real sequence by means of a point process technique which looks at a sequence of point processes based on (X sub n). Section 2 reviews some background on point processes and proves a convergence result about a sequence of point processes based on stationary variables which is flexible enough for our needs. Section 3 builds on this treatment to prove a convergence result about a sequence of point processes based on our moving averages.The authors give some remarks and some complementary extreme value results in Section 4. Included are discussions about convergence of maxima to extremal processes, the extremal index, exceedances, joint limit distributions of the largest and second largest as well as the largest and smallest among (X sub 1,..., X sub n). Section 5 discusses max-moving averages based on (Z sub i). Keywords: Random variables, Reprints, Exponential distribution. (kr)