## 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) |
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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 |
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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.