A local limit theorem for maxima of i.i.d. random variables is proved. Also it is shown that under the so-called von Mises' conditions the density of the normalized maximum converges to the limit density in $L_p(0 < p \leq \infty)$ provided both the original density and the limit density are in $L_p$. Finally an occupation time result is proved. The methods of proof are different from those used for the corresponding results concerning partial sums.
Publié le : 1982-05-14
Classification:
Local limit theorem,
extreme values,
regular variation,
occupation time,
density convergence,
60F05,
60F25
@article{1176993865,
author = {de Haan, L. and Resnick, S. I.},
title = {Local Limit Theorems for Sample Extremes},
journal = {Ann. Probab.},
volume = {10},
number = {4},
year = {1982},
pages = { 396-413},
language = {en},
url = {http://dml.mathdoc.fr/item/1176993865}
}
de Haan, L.; Resnick, S. I. Local Limit Theorems for Sample Extremes. Ann. Probab., Tome 10 (1982) no. 4, pp. 396-413. http://gdmltest.u-ga.fr/item/1176993865/