We establish Berry-Esseen type estimates for random variables with values in a real separable Hilbert space $H$. These estimates are then used to prove the law of the iterated logarithm for sequences of $H$-valued random variables and also to prove a functional form of the law of the iterated logarithm for $H$-valued partial sums as given by Strassen. We also prove a $\log \log$ result for $H$-valued symmetric stable random variables.
Publié le : 1974-06-14
Classification:
6008,
6030,
2846,
Abstract Wiener spaces,
measurable norm,
Gaussian measures norm,
Gaussian measures,
Strassen's Law of the Iterated Logarithm,
Berry-Esseen estimates,
Brownian motion
@article{1176996655,
author = {Kuelbs, J. and Kurtz, T.},
title = {Berry-Esseen Estimates in Hilbert Space and an Application to the Law of the Iterated Logarithm},
journal = {Ann. Probab.},
volume = {2},
number = {6},
year = {1974},
pages = { 387-407},
language = {en},
url = {http://dml.mathdoc.fr/item/1176996655}
}
Kuelbs, J.; Kurtz, T. Berry-Esseen Estimates in Hilbert Space and an Application to the Law of the Iterated Logarithm. Ann. Probab., Tome 2 (1974) no. 6, pp. 387-407. http://gdmltest.u-ga.fr/item/1176996655/