CENTRAL LIMIT PROBLEM FOR MIXING SEQUENCES OF RANDOM VARIABLES

In this paper the central limit problem is solved for sums of random variables having bounded variances and satisfying certain mixing conditions. In case of a stochastic process these mixing conditions essentially say that as time passes events concerning the future" of the process are almost independent from the events in the "past". It turns out that the class of limit laws for sums of mixing random variables is exactly the same as for the bounded variances case of independent random variables. We also shall give criteria for convergence to any specified law of this class of possible limit laws. Finally we shall derive the central limit theorem involving a kind of Lindeberg-Feller condition and as a corollary thereof a kind of Ljapounov theorem. © 1969 Springer-Verlag."