The Annals of Probability

Invariance Principles for Mixing Sequences of Random Variables

Magda Peligrad

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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

Permanent link to this document
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
links.jstor.org

Subjects
Primary: 60F05: Central limit and other weak theorems
Secondary: 60B10: Convergence of probability measures

Keywords
Invariance principles mixing sequences of random variables

Citation

Peligrad, Magda. Invariance Principles for Mixing Sequences of Random Variables. Ann. Probab. 10 (1982), no. 4, 968--981. doi:10.1214/aop/1176993718. http://projecteuclid.org/euclid.aop/1176993718.


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