We examine the cluster set of $S_n/a_n$ for Banach space valued random variables, and investigate the relationship between the central limit theorem and the law of the iterated logarithm in this setting. In the case of Hilbert space valued random variables, necessary and sufficient conditions are given for the law of the iterated logarithm. Some interesting examples are also included. We then apply our results to weighted empiricals both in the supremum norm and the $L^2\lbrack 0, 1\rbrack$ norm.
Publié le : 1981-10-14
Classification:
Law of the iterated logarithm,
cluster set,
central limit theorem,
60B05,
60F05,
60F10,
60F15,
28A40,
60B10
@article{1176994305,
author = {Goodman, V. and Kuelbs, J. and Zinn, J.},
title = {Some Results on the LIL in Banach Space with Applications to Weighted Empirical Processes},
journal = {Ann. Probab.},
volume = {9},
number = {6},
year = {1981},
pages = { 713-752},
language = {en},
url = {http://dml.mathdoc.fr/item/1176994305}
}
Goodman, V.; Kuelbs, J.; Zinn, J. Some Results on the LIL in Banach Space with Applications to Weighted Empirical Processes. Ann. Probab., Tome 9 (1981) no. 6, pp. 713-752. http://gdmltest.u-ga.fr/item/1176994305/