This paper considers how to measure the magnitude of the sum of
independent random variables in several ways. We give a formula for the tail
distribution for sequences that satisfy the so called Lévy property. We
then give a connection between the tail distribution and the pth moment,
and between the pth moment and the rearrangement invariant norms.
Publié le : 2001-02-14
Classification:
Sum of independent random variables,
tail distributions,
decreasing rearrangement,
pth moment,
rearrangement invariant space,
disjoint sum,
maximal function,
Hoffmann-Jørgensen/Klass-Nowicki Inequality,
Lévy Property,
60G50,
60E15,
46E30,
46B09
@article{1008956339,
author = {Hitczenko, Pawe\l\ and Montgomery-Smith, Stephen},
title = {Measuring the magnitude of sums of independent random
variables},
journal = {Ann. Probab.},
volume = {29},
number = {1},
year = {2001},
pages = { 447-466},
language = {en},
url = {http://dml.mathdoc.fr/item/1008956339}
}
Hitczenko, Paweł; Montgomery-Smith, Stephen. Measuring the magnitude of sums of independent random
variables. Ann. Probab., Tome 29 (2001) no. 1, pp. 447-466. http://gdmltest.u-ga.fr/item/1008956339/