For an i.i.d. sequence of random variables with a semiexponential
distribution, we give a functional form of the Erdös–Renyi law
for partial sums. In contrast to the classical case, that is, the case where
the random variables have exponential moments of all orders, the set of limit
points is not a subset of the continuous functions. This reflects the bigger
influence of extreme values. The proof is based on a large deviation principle
for the trajectories of the corresponding random walk. The normalization in
this large deviation principle differs from the usual normalization and depends
on the tail of the distribution. In the same way, we prove a functional limit
law for moving averages.
Publié le : 1998-07-14
Classification:
Erdös-Renyi laws,
large deviations,
semiexponential distributions,
moving averages,
random walks,
60F17,
60F10,
60G50
@article{1022855755,
author = {Gantert, Nina},
title = {Functional Erd\H os-Renyi laws for semiexponential random
variables},
journal = {Ann. Probab.},
volume = {26},
number = {1},
year = {1998},
pages = { 1356-1369},
language = {en},
url = {http://dml.mathdoc.fr/item/1022855755}
}
Gantert, Nina. Functional Erdős-Renyi laws for semiexponential random
variables. Ann. Probab., Tome 26 (1998) no. 1, pp. 1356-1369. http://gdmltest.u-ga.fr/item/1022855755/