Events The 1st International Online Conference on Mathematics and Applications

Event submissions

Published

10.3390/IOCMA2023-14423

This submission belongs to the session S7. Probability and Statistics of the event The 1st International Online Conference on Mathematics and Applications

Published date

28 Apr, 2023

Academic Editor

Antonio Di Crescenzo

Citation

Vitaly Sobolev, Sergey M. Ramodanov, On Estimation of the Remainder Term in New Asymptotic Expansions in the Central Limit Theorem, in Proceedings of The 1st International Online Conference on Mathematics and Applications, 1 May–15 May 2023, MDPI: Basel, Switzerland, doi: 10.3390/IOCMA2023-14423

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On Estimation of the Remainder Term in New Asymptotic Expansions in the Central Limit Theorem

Vitaly Sobolev ¹

Sergey M. Ramodanov ¹

1. Department of Probability Theory and Applied Mathematics; Moscow Technical University of Communications and Informatics

Abstract

We offer a new asymptotic expansion with explicit remainder estimate in the central limit theorem. The results obtained are essentially based on the ideas of the paper. We also present a more accurate estimation of the CLT-expansions remainder which is rigorously proved and backed up numerically. It is shown that our approach can be used for further refinement of allied asymptotic expansions

Keywords

central limit theorem

asymptotic expansion

random variables

characteristic function

accuracy of approximation

approximation exactness

estimates for the exactness of approximation

distribution of probabilities

Manuscript

Sob_Rom_iocma2023_1.pdf

Stochastic Boundary Value Problems via Wiener-Chaos Expansion

Mathematical analysis of a discrete system modeling COVID-19.