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Volume 8
Issue 4
10.3390/math8040479
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Article

Rates of Convergence in Laplace’s Integrals and Sums and Conditional Central Limit Theorems

by
Vassili N. Kolokoltsov
Department of Statistics, University of Warwick, Coventry CV4 7AL, UK
Mathematics 2020, 8(4), 479; https://doi.org/10.3390/math8040479
Submission received: 28 February 2020 / Revised: 27 March 2020 / Accepted: 30 March 2020 / Published: 1 April 2020
(This article belongs to the Special Issue Stability Problems for Stochastic Models: Theory and Applications)
Versions Notes

Abstract

We obtained the exact estimates for the error terms in Laplace’s integrals and sums implying the corresponding estimates for the related laws of large number and central limit theorems including the large deviations approximation.
Keywords: integrals and sums; rates of convergence; conditional law of large numbers; conditional central limit theorem integrals and sums; rates of convergence; conditional law of large numbers; conditional central limit theorem

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MDPI and ACS Style

Kolokoltsov, V.N. Rates of Convergence in Laplace’s Integrals and Sums and Conditional Central Limit Theorems. Mathematics 2020, 8, 479. https://doi.org/10.3390/math8040479

AMA Style

Kolokoltsov VN. Rates of Convergence in Laplace’s Integrals and Sums and Conditional Central Limit Theorems. Mathematics. 2020; 8(4):479. https://doi.org/10.3390/math8040479

Chicago/Turabian Style

Kolokoltsov, Vassili N. 2020. "Rates of Convergence in Laplace’s Integrals and Sums and Conditional Central Limit Theorems" Mathematics 8, no. 4: 479. https://doi.org/10.3390/math8040479

APA Style

Kolokoltsov, V. N. (2020). Rates of Convergence in Laplace’s Integrals and Sums and Conditional Central Limit Theorems. Mathematics, 8(4), 479. https://doi.org/10.3390/math8040479

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