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Non-uniform bounds in local limit theorems in case of fractional moments. I. (English) Zbl 1239.60016
Summary: Edgeworth-type expansions for convolutions of probability densities and powers of the characteristic functions with non-uniform error terms are established for i.i.d. random variables with finite (fractional) moments of order \(s \geq 2\), where \(s\) may be not an integer.

60F05 Central limit and other weak theorems
60E10 Characteristic functions; other transforms
Full Text: DOI
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