In this paper we prove a theorem on the convergence rate in the Marcinkiewicz-Zygmund strong law for stationary mixing sequences. Our result gives the $r$-quick strong law and the finiteness of moments of the largest excess of boundary crossings for such sequences.
Publié le : 1977-10-14
Classification:
Convergence rates,
$r$-quick strong law,
stationary sequences,
$\varphi$-mixing,
strong mixing,
moment conditions,
large deviations,
60F10,
60F15
@article{1176995713,
author = {Lai, Tze Leung},
title = {Convergence Rates and $r$-Quick Versions of the Strong Law for Stationary Mixing Sequences},
journal = {Ann. Probab.},
volume = {5},
number = {6},
year = {1977},
pages = { 693-706},
language = {en},
url = {http://dml.mathdoc.fr/item/1176995713}
}
Lai, Tze Leung. Convergence Rates and $r$-Quick Versions of the Strong Law for Stationary Mixing Sequences. Ann. Probab., Tome 5 (1977) no. 6, pp. 693-706. http://gdmltest.u-ga.fr/item/1176995713/