We prove a small deviation theorem of a new form for the functional central limit theorem for partial sums of independent, identically distributed finite-dimensional random vectors. The result is applied to obtain a functional form of the Chung-Jain-Pruitt law of the iterated logarithm which is also a strong speed of convergence theorem refining Strassen's invariance principle.
Publié le : 1983-02-14
Classification:
Small deviations,
other law of the iterated logarithm,
Strassen's invariance principle,
60F15
@article{1176993661,
author = {de Acosta, Alejandro},
title = {Small Deviations in the Functional Central Limit Theorem with Applications to Functional Laws of the Iterated Logarithm},
journal = {Ann. Probab.},
volume = {11},
number = {4},
year = {1983},
pages = { 78-101},
language = {en},
url = {http://dml.mathdoc.fr/item/1176993661}
}
de Acosta, Alejandro. Small Deviations in the Functional Central Limit Theorem with Applications to Functional Laws of the Iterated Logarithm. Ann. Probab., Tome 11 (1983) no. 4, pp. 78-101. http://gdmltest.u-ga.fr/item/1176993661/