Strong approximation for set-indexed partial sum processes via KMT constructions III
Rates of convergence for minimal distances in the central limit theorem under projective criteria.
About the Lindeberg method for strongly mixing sequences
Une inégalité de Bennett pour les maxima de processus empiriques
Upper bounds for minimal distances in the central limit theorem
We obtain upper bounds for minimal metrics in the central limit theorem for sequences of independent real-valued random variables.
Covariance inequalities for strongly mixing processes
About the Lindeberg method for strongly mixing sequences
We extend the Lindeberg method for the central limit theorem to strongly mixing sequences. Here we obtain a generalization of the central limit theorem of Doukhan, Massart and Rio to nonstationary strongly mixing triangular arrays. The method also provides estimates of the Lévy distance between the distribution of the normalized sum and the standard normal.
On mean central limit theorems for stationary sequences
In this paper, we give estimates of the minimal distance between the distribution of the normalized partial sum and the limiting gaussian distribution for stationary sequences satisfying projective criteria in the style of Gordin or weak dependence conditions.
On the functional central limit theorem for stationary processes
The functional central limit theorem for strongly mixing processes
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