## 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

### MSC:

 60F05 Central limit and other weak theorems 60G10 Stationary stochastic processes
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