Invariance Principles for Mixing Sequences of Random Variables

In this note we prove weak invariance principles for some classes of mixing sequences of L₂-integrable random variables under the condition that the variance of the sum of n random variables is asymptotic to σ²n where σ² > 0. One of the results is simultaneously an extension to nonstationary case of a theorem of Ibragimov and an improvement of the φ-mixing rate used by McLeish in his invariance principle for nonstationary φ-mixing sequences.