A central limit theorem for non stationary mixing processes. (English) Zbl 0685.60022

For a non-stationary \(\alpha\)-mixing sequence of random variables for which the variance of partial sums tends to infinity for \(n\to \infty\) and the maximum of the variances of variables divided by the variance of partial sums converges to zero, the author gives a necessary and sufficient condition for the central limit theorem.
The condition is expressed in a form of uniform integrability of squares of normalized partial sums. The idea of the proof is to approximate the above mentioned normalized sum by a partition of the set of positive numbers \(\{\) 1,...,n\(\}\).
Reviewer: J.Á.Víšek


60F05 Central limit and other weak theorems
60G10 Stationary stochastic processes
Full Text: EuDML