A strong law of large numbers is proved for tight, independent random elements (in a separable normed linear space) which have uniformly bounded $p$th moments $(p > 1)$. In addition, a weak law of large numbers is obtained for tight random elements with uniformly bounded $p$th moments $(p > 1)$ where convergence in probability for the separable normed linear space holds if and only if convergence in probability for the weak linear topology holds.
Publié le : 1979-02-14
Classification:
Law of large numbers,
random elements,
tightness,
convergence in probability,
convergence with probability one,
compactness,
60B05,
60F15,
60G99
@article{1176995156,
author = {Taylor, R. L. and Wei, Duan},
title = {Laws of Large Numbers for Tight Random Elements in Normed Linear Spaces},
journal = {Ann. Probab.},
volume = {7},
number = {6},
year = {1979},
pages = { 150-155},
language = {en},
url = {http://dml.mathdoc.fr/item/1176995156}
}
Taylor, R. L.; Wei, Duan. Laws of Large Numbers for Tight Random Elements in Normed Linear Spaces. Ann. Probab., Tome 7 (1979) no. 6, pp. 150-155. http://gdmltest.u-ga.fr/item/1176995156/