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**Recent advances in the central limit theorem and its weak invariance principle for mixing sequences of random variables (a survey).**
*(English)*
Zbl 0603.60022

Dependence in probability and statistics, Conf. Oberwolfach 1985, Prog. Probab. Stat. 11, 193-223 (1986).

[For the entire collection see Zbl 0591.00012.]

The paper presents the progress that has recently been made in the study of the central limit theorem and its weak invariance principle for mixing sequences of random variables. For the sake of simplicity all results are stated for centered strictly stationary or centered second order stationary sequences. Three important classes of mixing sequences i.e. strong mixing, \(\rho\)-mixing and \(\phi\)-mixing are treated separately. Also several open problems and conjectures in the subject are formulated and discussed. The presentation of the results is clear and comprehensive.

The paper presents the progress that has recently been made in the study of the central limit theorem and its weak invariance principle for mixing sequences of random variables. For the sake of simplicity all results are stated for centered strictly stationary or centered second order stationary sequences. Three important classes of mixing sequences i.e. strong mixing, \(\rho\)-mixing and \(\phi\)-mixing are treated separately. Also several open problems and conjectures in the subject are formulated and discussed. The presentation of the results is clear and comprehensive.

Reviewer: T.Inglot

### MSC:

60F05 | Central limit and other weak theorems |

60F17 | Functional limit theorems; invariance principles |