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 $m$.
Publié le : 1975-02-14
Classification:
Extremal processes,
convergence of finite-dimensional laws,
stationary transition probabilities,
60K99,
60J25,
62E20,
62G30
@article{1176996459,
author = {Weissman, Ishay},
title = {Extremal Processes Generated by Independent Nonidentically Distributed Random Variables},
journal = {Ann. Probab.},
volume = {3},
number = {6},
year = {1975},
pages = { 172-177},
language = {en},
url = {http://dml.mathdoc.fr/item/1176996459}
}
Weissman, Ishay. Extremal Processes Generated by Independent Nonidentically Distributed Random Variables. Ann. Probab., Tome 3 (1975) no. 6, pp. 172-177. http://gdmltest.u-ga.fr/item/1176996459/