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

Bradley, Richard C.

Ann. Probab. 16, No. 1, 313-332 (1988).

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

MSC:

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

Keywords:

infinite variance; central limit theorem; strictly stationary sequences

Citations:

Zbl 0219.60027