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August, 1977 On the Invariance Principle for Nonstationary Mixingales
D. L. McLeish
Ann. Probab. 5(4): 616-621 (August, 1977). DOI: 10.1214/aop/1176995772


In an earlier paper, the author proves an invariance principle for mixingales, a generalization of the concepts of mixing sequences and martingale differences, under the condition that the variance of the sum of $n$ random variables is asymptotic to $\sigma^2n$ where $\sigma^2 > 0$. In this note we relax further the required degree of stationarity, requiring only that the squared variables properly normalized form a uniformly integrable family, and the partial sums have variances consistent with the Wiener process.


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D. L. McLeish. "On the Invariance Principle for Nonstationary Mixingales." Ann. Probab. 5 (4) 616 - 621, August, 1977.


Published: August, 1977
First available in Project Euclid: 19 April 2007

zbMATH: 0367.60021
MathSciNet: MR445583
Digital Object Identifier: 10.1214/aop/1176995772

Primary: 60F05
Secondary: 60G45

Keywords: central limit theorem , Invariance principles , Mixing

Rights: Copyright © 1977 Institute of Mathematical Statistics

Vol.5 • No. 4 • August, 1977
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