In this paper we describe a general device that allows us to deduce various kinds of theorems (moment estimates, exponential inequalities, strong law of large numbers, stability results, bounded law of the iterated logarithm) for partial sums of independent vector-valued random variables from related results for partial sums of independent real-valued random variables. The concept of majorization will play a key role in our considerations.
Publié le : 1991-07-14
Classification:
Majorization,
moment inequalities,
exponential inequalities,
strong law of large numbers,
bounded law of the iterated logarithm,
60B12,
60F10,
60F15,
60E15,
60G50
@article{1176990341,
author = {Berger, Erich},
title = {Majorization, Exponential Inequalities and Almost Sure Behavior of Vector-Valued Random Variables},
journal = {Ann. Probab.},
volume = {19},
number = {4},
year = {1991},
pages = { 1206-1226},
language = {en},
url = {http://dml.mathdoc.fr/item/1176990341}
}
Berger, Erich. Majorization, Exponential Inequalities and Almost Sure Behavior of Vector-Valued Random Variables. Ann. Probab., Tome 19 (1991) no. 4, pp. 1206-1226. http://gdmltest.u-ga.fr/item/1176990341/