We investigate the cluster set $C(\{S_n/a_n\})$ under conditions necessary for the bounded law of the iterated logarithm, and obtain necessary and sufficient conditions for the LIL in spaces satisfying a certain comparison principle. In particular, these results settle some previously unanswered questions in the Hilbert space setting.
Publié le : 1983-02-14
Classification:
Law of the iterated logarithm,
cluster set,
smooth norm spaces,
type 2 space,
upper Gaussian comparison principle,
60B05,
60B11,
60B12,
60F10,
60F15,
28C20,
60B10
@article{1176993662,
author = {de Acosta, A. and Kuelbs, J.},
title = {Some Results on the Cluster Set $C\bigg(\bigg{\frac{S\_n}{a\_n}\bigg}\bigg)$ and the LIL},
journal = {Ann. Probab.},
volume = {11},
number = {4},
year = {1983},
pages = { 102-122},
language = {en},
url = {http://dml.mathdoc.fr/item/1176993662}
}
de Acosta, A.; Kuelbs, J. Some Results on the Cluster Set $C\bigg(\bigg{\frac{S_n}{a_n}\bigg}\bigg)$ and the LIL. Ann. Probab., Tome 11 (1983) no. 4, pp. 102-122. http://gdmltest.u-ga.fr/item/1176993662/