Characteristic Functions

Sergey Bobkov; Gennadiy Chistyakov; Friedrich Götze

doi:10.1007/978-3-031-31149-9_3

Characteristic Functions

Sergey Bobkov, Gennadiy Chistyakov, Friedrich Götze

Mathematics

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Abstract

The moment functionals we discussed before may be explicitly expressed in terms of characteristic functions of linear functionals of a given random vector. However, information on various bounds on characteristic functions and their deviations from the characteristic function of another law on the real line will be needed for a different purpose – to study the Kolmogorov and Lévy distances between the corresponding distribution functions. In this chapter, we describe general tools in the form of smoothing and Berry–Esseen-type inequalities, which allow one to perform the transition from the results about closeness or smallness of Fourier–Stieltjes transforms to corresponding results about the associated functions of bounded variation.

Original language	English (US)
Title of host publication	Probability Theory and Stochastic Modelling
Publisher	Springer Nature
Pages	51-62
Number of pages	12
DOIs	https://doi.org/10.1007/978-3-031-31149-9_3
State	Published - 2023

Publication series

Name	Probability Theory and Stochastic Modelling
Volume	104
ISSN (Print)	2199-3130
ISSN (Electronic)	2199-3149

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© 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.

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T1 - Characteristic Functions

AU - Bobkov, Sergey

AU - Chistyakov, Gennadiy

AU - Götze, Friedrich

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Characteristic Functions

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