A functional central limit theorem for \(\rho\) -mixing sequences
In this note a functional central limit theorem for \(\rho\) -mixing sequences of \textit{I. A. Ibragimov} [Teor. Veroyatn. Primen. 20, 134-140 (1975; Zbl 0335.60023); English translation in Theory Probab. Appl. 20, 135-141 (1975)] is generalized to non-stationary sequences \((X_ n)_{n\in {\mathbb{N}}}\), satisfying some assumptions on the variances and the moment condition \(E| X_ n|^{2+b}=0(n^{b/2-\epsilon})\) for some \(b>0\), \(\epsilon >0\). The main step in the argument is the proof of a suitable estimate for \(E|\sum^{n}_{i=1}X_ i|^{2+b}\).
scientific article; zbMATH DE number 3872385