In this note we prove weak invariance principles for some classes of mixing sequences of $L_2$-integrable random variables under the condition that the variance of the sum of $n$ random variables is asymptotic to $\sigma^2n$ where $\sigma^2 > 0$. One of the results is simultaneously an extension to nonstationary case of a theorem of Ibragimov and an improvement of the $\varphi$-mixing rate used by McLeish in his invariance principle for nonstationary $\varphi$-mixing sequences.
Publié le : 1982-11-14
Classification:
Invariance principles,
mixing sequences of random variables,
60F05,
60B10
@article{1176993718,
author = {Peligrad, Magda},
title = {Invariance Principles for Mixing Sequences of Random Variables},
journal = {Ann. Probab.},
volume = {10},
number = {4},
year = {1982},
pages = { 968-981},
language = {en},
url = {http://dml.mathdoc.fr/item/1176993718}
}
Peligrad, Magda. Invariance Principles for Mixing Sequences of Random Variables. Ann. Probab., Tome 10 (1982) no. 4, pp. 968-981. http://gdmltest.u-ga.fr/item/1176993718/