Approximation of convolutions of multi-dimensional symmetric distributions by accompanying laws

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Abstract

Let F be a symmetric k-dimensional probability distribution, whose characteristic function {Mathematical expression} satisfies for all t ∈Rk the inequality {Mathematical expression} ≥ -1 + α, where 0 < α < 2. Let n be an arbitrary natural number, let Fn 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(Fn,e(nF))≤c1(k)(n-1+exp(-nα+ckℓn3n)), where c1(k) depends only on the dimension k, while c2is an absolute constant.

Translated title of the contributionОб аппроксимации сверток многомерных симметричных распределений сопровождающими законами
Original languageEnglish
Pages (from-to)1859-1872
Number of pages14
JournalJournal of Soviet Mathematics
Volume61
Issue number1
DOIs
StatePublished - 1 Aug 1992

Scopus subject areas

  • Mathematics(all)

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