On the Invariance Principle for Nonstationary Mixingales

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 σ²n where σ² > 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.