Geodesic
Variance inequalities for covariance kernels and applications to central limit theorems
Teoriâ veroâtnostej i ee primeneniâ, Tome 42 (1997) no. 1, pp. 195-201

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A simple estimate for the error in the CLT, valid for a wide class of absolutely continuous r.v.'s, is derived without Fourier techniques. This is achieved by using a simple convolution inequality for the variance of covariance kernels or w-functions in conjunction with bounds for the total variation distance. The results are extended to the multivariate case. Finally, a simple proof of the classical Darmois–Skitovich characterization of normality is obtained.
Keywords: convolution inequality, CLT, rate of convergence, characterization of normality.
Mots-clés : covariance kernels 
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     title = {Variance inequalities for covariance kernels and applications to central limit theorems},
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T. Cacoullos; N. Papadatos; V. Papathanasiou. Variance inequalities for covariance kernels and applications to central limit theorems. Teoriâ veroâtnostej i ee primeneniâ, Tome 42 (1997) no. 1, pp. 195-201. http://geodesic.mathdoc.fr/item/TVP_1997_42_1_a14/