Estimation of the rate of convergence in the central limit theorem for a sequence of series in terms of averaged pseudomoments

Authors:
M. M. Kapustei and P. V. Slyusarchuk

Translated by:
S. V. Kvasko

Original publication:
Teoriya Imovirnostei ta Matematichna Statistika, tom **99** (2018).

Journal:
Theor. Probability and Math. Statist. **99** (2019), 101-111

MSC (2010):
Primary 60F05

DOI:
https://doi.org/10.1090/tpms/1083

Published electronically:
February 27, 2020

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: A generalization of Zolotarev's estimates is proved for a sequence of series of random variables. The estimates are expressed in terms of averaged pseudomoments.

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Additional Information

**M. M. Kapustei**

Affiliation:
Department of Probability Theory and Mathematical Analysis, Faculty for Mathematics, Uzhgorod National University, Universytets’ka Street, 14, Uzhgorod, 88020 Ukraine

Email:
michaelkapustey@gmail.com

**P. V. Slyusarchuk**

Affiliation:
Department of Probability Theory and Mathematical Analysis, Faculty for Mathematics, Uzhgorod National University, Universytets’ka Street, 14, Uzhgorod, 88020 Ukraine

Email:
petro_slyusarchuk@ukr.net

DOI:
https://doi.org/10.1090/tpms/1083

Keywords:
Convergence,
central limit theorem,
pseudomoments,
sequence of series,
nonidentically distributed random variables

Received by editor(s):
June 25, 2018

Published electronically:
February 27, 2020

Article copyright:
© Copyright 2020
American Mathematical Society