Abstract.
This paper is devoted to the rate of convergence problem in the central limit theorem for sums of independent identically distributed random variables with regular probability density function. The method we use depends strictly on Fourier based metrics, and yields Berry-Esseen like bounds for the convergence towards both a normal and a stable law in various Sobolev norms.
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Received 31 May 2001; in revised form 13 November 2001
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Goudon, T., Junca, S. & Toscani, G. Fourier-Based Distances and Berry-Esseen Like Inequalities for Smooth Densities. Mh Math 135, 115–136 (2002). https://doi.org/10.1007/s006050200010
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DOI: https://doi.org/10.1007/s006050200010