Berry–Esseen for Free Random Variables

Vladislav Kargin ()

Journal of Theoretical Probability, 2007, vol. 20, issue 2, 381-395

Abstract: Abstract An analogue of the Berry–Esseen inequality is proved for the speed of convergence of free additive convolutions of bounded probability measures. The obtained rate of convergence is of the order n −1/2, the same as in the classical case. An example with binomial measures shows that this estimate cannot be improved without imposing further restrictions on convolved measures.

Keywords: Berry–Esseen inequality; Free probability; Central limit theorem; Speed of convergence (search for similar items in EconPapers)
Date: 2007
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DOI: 10.1007/s10959-007-0097-7

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