On quantiles and the central limit question for strongly mixing sequences
The author constructs three classes of strictly stationary strongly mixing random sequences in order to throw further light on the ``borderline'' of the central limit theorem for strictly stationary, strongly mixing random sequences. These examples involve the combining of ideas from the ``renewal type'' Markov chains that Davydov (1969, 1973) used as the basis for his counterexamples to the CLT, Barbee (1981), Herrndorf (1983) and Doukhan, Massart and Rio (1994). In particular in these constructions, a key role is played by quantiles in the central limit theorem under strong mixing -- a theme that was developed by Doukhan et al. (1994), on the basis of a covariance inequality proved by Rio (1993).
scientific article; zbMATH DE number 1071665