The growth rate of partial maxima on subsequences (Q1060765)

The growth rate of partial maxima M(n) for i.i.d. random variables is considered with respect to subsequences \(\{n_ k\}\). To find explicit results we deal with a certain class of random variables where explicit results are known for the growth of M(n). We show that only the maximal growth of \(M(n_ k)\) is influenced by the growth rate of the given subsequence \(\{n_ k\}\). We give results with respect to a general and two special conditions on the growth of the subsequences.