Central limit theorem for finitely-dependent random variables

For sequences of finitely-dependent random variables, under rather general hypotheses we establish estimates of integrals of the form where F_n(x) is the distribution function of the normalized sum of random variables; (x) is the standard normal distribution function. In the proof we use relations obtained by the method of C. Stein. The results are applicable, in particular, to m-dependent random variables and fields.Translated from Teoriya Sluchainykh Protsessov, No. 16, pp. 93–97, 1988.