Resumen de Limit laws for maxima of a stationary random sequence with random sample size

A. Freitas, Jürg Hüsler, M. Graça Temido

• Let {X n } be a stationary sequence and {k n } be a nondecreasing sequence such that k n+1/k n →r≥1. Assume that the limit distribution G of Mkn with an appropriate linear normalization exists. We consider the maxima M n =max {X i ,i≤n} sampled at random times T n , where T n /k n converges in probability to a positive random variable D, and show that the limit distribution of MTn exists under weak mixing conditions. The limit distribution of MTn is a mixture of G and the distribution of D.