Limit Laws for Maxima and Second Maxima from Strong-Mixing Processes

Abstract

In 1972, R. E. Welsch obtained a class of two-dimensional laws which includes the class of all possible limit laws for a sequence of normalized pairs $(M_n, S_n)$, where $M_n$ and $S_n$ are the maximum and the second maximum of the first $n$ terms from a stationary strong-mixing sequence of random variables. In this note an example is given to show that these two classes are identical.