Under some mild regularity on the normalizing sequence, we obtain
necessary and sufficient conditions for the strong law of large numbers for
(symmetrized) U-statistics.We also obtain necessary and sufficient
conditions for the a.s. convergence of series of an analogous form.
Publié le : 2000-10-14
Classification:
U-statistics,
strong law of large numbers,
random series,
60F15,
60E15
@article{1019160513,
author = {Lata\l a, Rafa\l\ and Zinn, Joel},
title = {Necessary and sufficient conditions for the strong law of large
numbers for U-statistics},
journal = {Ann. Probab.},
volume = {28},
number = {1},
year = {2000},
pages = { 1908-1924},
language = {en},
url = {http://dml.mathdoc.fr/item/1019160513}
}
Latała, Rafał; Zinn, Joel. Necessary and sufficient conditions for the strong law of large
numbers for U-statistics. Ann. Probab., Tome 28 (2000) no. 1, pp. 1908-1924. http://gdmltest.u-ga.fr/item/1019160513/