## Abstract

Let F be a symmetric k-dimensional probability distribution, whose characteristic function {Mathematical expression} satisfies for all t ∈R^{k} the inequality {Mathematical expression} ≥ -1 + α, where 0 < α < 2. Let n be an arbitrary natural number, let F^{n} be the n-fold convolution of the distribution F with itself, and let e(nF) be the accompanying infinitely divisible distribution with characteristic function exp(n( {Mathematical expression} -1)). It is proved that the uniform distance ρ(·,·) between corresponding distribution functions admits estimate ρ(F^{n},e(nF))≤c_{1}(k)(n^{-1}+exp(-nα+c_{ℓ}kℓn^{3}n)), where c_{1}(k) depends only on the dimension k, while c_{2}is an absolute constant.

Translated title of the contribution | Об аппроксимации сверток многомерных симметричных распределений сопровождающими законами |
---|---|

Original language | English |

Pages (from-to) | 1859-1872 |

Number of pages | 14 |

Journal | Journal of Soviet Mathematics |

Volume | 61 |

Issue number | 1 |

DOIs | |

State | Published - 1 Aug 1992 |

## Scopus subject areas

- Mathematics(all)