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 | |
| State | Published - 2023 |
Publication series
| Name | Probability Theory and Stochastic Modelling |
|---|---|
| Volume | 104 |
| ISSN (Print) | 2199-3130 |
| ISSN (Electronic) | 2199-3149 |
Bibliographical note
Publisher Copyright:© 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.