## The Annals of Probability

### Invariance Principles for Mixing Sequences of Random Variables

#### Abstract

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.

#### Article information

Source
Ann. Probab. Volume 10, Number 4 (1982), 968-981.

Dates
First available in Project Euclid: 19 April 2007

http://projecteuclid.org/euclid.aop/1176993718

Digital Object Identifier
doi:10.1214/aop/1176993718

Mathematical Reviews number (MathSciNet)
MR672297

Zentralblatt MATH identifier
0503.60044

JSTOR