Approximation by infinitely divisible distributions in the multidimensional caseстатья
Информация о цитировании статьи получена из
Scopus
Статья опубликована в журнале из списка Web of Science и/или Scopus
Дата последнего поиска статьи во внешних источниках: 23 ноября 2017 г.
Аннотация:Let P be the collection of parallelepipeds in R^κ with edges parallel with the coordinate axes and let
be the collection of closed sets in Rκ. Let π(G, H)=inf {ε∣ G{A}⩽H{Aε}+ε, H{A}⩽G{Aε}+ε for any Borel set A; L(G, H) = inf {ε∣ G{A}⩽H{A^ε}+ε, H{A}⩽G{A^ε}+ε for any A in P, where G, H are distributions in R^κ, A^ε={x∈R^κ : inf_{y∈A} ∥x−y∥<ε}. In the paper one gives the proofs of results announced earlier by the author (Dokl. Akad. Nauk SSSR, 253, No. 2, 277–279 (1980)). One considers the problem of the approximation of the distributions of sums of independent random vectors with the aid of infinitely divisible distributions. One obtains estimates for the distances π(·, ·), L(·, ·).