Abstract
Let \(F_n\) denote the distribution function of the normalized sum \(Z_n = (X_1 + \cdots + X_n)/(\sigma \sqrt{n})\) of i.i.d. random variables with finite fourth absolute moment. In this paper, polynomial rates of convergence of \(F_n\) to the normal law with respect to the Kolmogorov distance, as well as polynomial approximations of \(F_n\) by the Edgeworth corrections (modulo logarithmically growing factors in n), are given in terms of the characteristic function of \(X_1\). Particular cases of the problem are discussed in connection with Diophantine approximations.
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Partially supported by the NSF Grant DMS-1612961.
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Bobkov, S.G. Central Limit Theorem and Diophantine Approximations. J Theor Probab 31, 2390–2411 (2018). https://doi.org/10.1007/s10959-017-0770-4
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DOI: https://doi.org/10.1007/s10959-017-0770-4