Extremal Processes Generated by Independent Nonidentically Distributed Random Variables

Abstract

Let $M_n = \max\{X_1, \cdots, X_n\}$ and $m_n(t) = (M_{\lbrack nt\rbrack} - a_n)/b_n(t \geqq 1/n)$, where the $\{X_i\}$ are independent rv's and $a_n$ and $b_n > 0$ are real constants. Suppose all the finite-dimensional laws of $m_n$ converge to those of a stochastic process $m = \{m(t): t > 0\}$. This paper is a study of the class of all such processes $m$.