We establish strong invariance principles for sums of stationary and ergodic processes with nearly optimal bounds. Applications to linear and some nonlinear processes are discussed. Strong laws of large numbers and laws of the iterated logarithm are also obtained under easily verifiable conditions.
Publié le : 2007-11-14
Classification:
Short- and long-range dependence,
strong convergence,
nonlinear time series,
martingale,
linear process,
law of the iterated logarithm,
strong invariance principle,
60F05,
60F17
@article{1191860422,
author = {Wu, Wei Biao},
title = {Strong invariance principles for dependent random variables},
journal = {Ann. Probab.},
volume = {35},
number = {1},
year = {2007},
pages = { 2294-2320},
language = {en},
url = {http://dml.mathdoc.fr/item/1191860422}
}
Wu, Wei Biao. Strong invariance principles for dependent random variables. Ann. Probab., Tome 35 (2007) no. 1, pp. 2294-2320. http://gdmltest.u-ga.fr/item/1191860422/