We establish the central limit theorem for linear processes with dependent innovations including martingales and mixingale type of assumptions as defined in McLeish [Ann. Probab. 5 (1977) 616–621] and motivated by Gordin [Soviet Math. Dokl. 10 (1969) 1174–1176]. In doing so we shall preserve the generality of the coefficients, including the long range dependence case, and we shall express the variance of partial sums in a form easy to apply. Ergodicity is not required.
Publié le : 2006-07-14
Classification:
Ergodic theorem,
central limit theorem,
stationary linear process,
martingale,
60F05,
60G10,
60G42,
60G48
@article{1158673330,
author = {Peligrad, Magda and Utev, Sergey},
title = {Central limit theorem for stationary linear processes},
journal = {Ann. Probab.},
volume = {34},
number = {1},
year = {2006},
pages = { 1608-1622},
language = {en},
url = {http://dml.mathdoc.fr/item/1158673330}
}
Peligrad, Magda; Utev, Sergey. Central limit theorem for stationary linear processes. Ann. Probab., Tome 34 (2006) no. 1, pp. 1608-1622. http://gdmltest.u-ga.fr/item/1158673330/