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On asymptotic expansion of the moments of smooth functions in the central limit theorem. (English. Russian original) Zbl 0889.60020
Sib. Math. J. 37, No. 3, 447-453 (1996); translation from Sib. Mat. Zh. 37, No. 3, 519-525 (1996).
The authors distinguish the second term in the asymptotic expansion for the expectations of smooth functions of sums of independent identically distributed random variables; moreover, the order of smallness of the remainder is optional. The method proposed in this article allows strengthening sometimes the corresponding results of the predecessors, while enlarging the class of smooth functions under fixed moment conditions.

60F05 Central limit and other weak theorems
Full Text: DOI
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