Limit Theorems for the Maximum Term of a Stationary Process

Abstract

This paper contains necessary and sufficient conditions, which sometimes coincide, for the limiting distribution of a uniformly (or strongly) mixing stationary process to be the same as for the independent process with the same marginal distributions. Examples with different limits are given. Let $H$ be any distribution function and let $c_n(\xi) = \inf \{x \in R: H(x) \geqq 1 - \xi/n\}$. The limiting behavior of $H^n(c_n(\xi))$ is determined.