Extremal Processes Generated by Independent Nonidentically Distributed Random Variables

Weissman, Ishay

Ann. Probab., Tome 3 (1975) no. 6, p. 172-177 / Harvested from Project Euclid

Résumé

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 $m$.

Détail

Publié le : 1975-02-14
Classification:  Extremal processes,  convergence of finite-dimensional laws,  stationary transition probabilities,  60K99,  60J25,  62E20,  62G30