Lamperti in 1964 showed that the convergence of the marginals of an extremal process generated by independent and identically distributed random variables implies the full weak convergence in the Skorohod $J_1$-topology. This result is generalized to the $k$th extremal process and to random variables which need not be identically distributed. The proof here is based on the weak convergence of a certain point-process (which counts the number of up-crossings of the variables) to a two-dimensional nonhomogeneous Poisson process.
Publié le : 1976-06-14
Classification:
Extremal processes,
multivariate $k$-dimensional extremal processes,
nonhomogeneous two-dimensional Poisson process,
$D\lbrack a, b \rbrack$ space,
Skorohod space of functions with several parameters,
weak convergence,
60B10,
60G99
@article{1176996096,
author = {Weissman, Ishay},
title = {On Weak Convergence of Extremal Processes},
journal = {Ann. Probab.},
volume = {4},
number = {6},
year = {1976},
pages = { 470-473},
language = {en},
url = {http://dml.mathdoc.fr/item/1176996096}
}
Weissman, Ishay. On Weak Convergence of Extremal Processes. Ann. Probab., Tome 4 (1976) no. 6, pp. 470-473. http://gdmltest.u-ga.fr/item/1176996096/