A central limit theorem for stationary \(\rho\)-mixing sequences with infinite variance. (English) Zbl 0643.60018

A central limit theorem is proved for strictly stationary sequences \(X_ 1,X_ 2,..\). which are weakly dependent in the sense of \(\rho\)-mixing (maximal correlation). The \(\rho\)-mixing coefficients \(\rho\) (n) are assumed to satisfy \(\rho (1)<1\) and \(\rho (2^ k)\) summable (which is essentially the slowest possible rate at which \(\rho\) (n) must converge to zero in order to obtain the result).
If the marginal distribution of \(X_ 1\) satisfies the classical tail conditions [see I. A. Ibragimov and Y. V. Linnik, Independent and stationary sequences of random variables (1971; Zbl 0219.60027), p. 83], then the partial sums are attracted to a normal law.
Reviewer: Ch.Hipp


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


Zbl 0219.60027
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