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.
Citation
Magda Peligrad. "Invariance Principles for Mixing Sequences of Random Variables." Ann. Probab. 10 (4) 968 - 981, November, 1982. https://doi.org/10.1214/aop/1176993718
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