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Teoriya Veroyatnostei i ee Primeneniya, 2022, Volume 67, Issue 1, Pages 3–22
DOI: https://doi.org/10.4213/tvp5416 (Mi tvp5416) 		 
This article is cited in 2 scientific papers (total in 2 papers)

On alternative approximating distributions in the multivariate version of Kolmogorov's second uniform limit theorem

F. Götzea, A. Yu. Zaitsevbc

a Fakultät für Mathematik, Universität Bielefeld, Bielefeld, Germany
b St. Petersburg Department of V. A. Steklov Institute of Mathematics, USSR Academy of Sciences
c Saint Petersburg State University
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DOI: https://doi.org/10.4213/tvp5416
Abstract: The aim of the present work is to show that our recent results on the approximation of distributions of sums of independent summands by the infinitely divisible laws on convex polyhedra can be obtained via an alternative class of approximating infinitely divisible distributions. We will also generalize the results to the infinite-dimensional case.
Keywords: Kolmogorov's uniform limit theorem, multidimensional distribution, infinitely divisible approximation, convex polyhedra.
Funding agency Grant number
Sonderforschungsbereich Topological and Correlated Electronics at Surfaces and Interfaces 1283
Russian Foundation for Basic Research 20-51-12004
19-01-00356
This work was supported by the SFB 1283 and by RFBR-DFG grant 20-51-12004. The second author was supported by RFBR grant 19-01-00356.
Received: 04.06.2020
Revised: 09.02.2021
Accepted: 01.12.2020
English version:
Theory of Probability and its Applications, 2022, Volume 67, Issue 1, Pages 1–16
DOI: https://doi.org/10.1137/S0040585X97T99071X
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: F. Götze, A. Yu. Zaitsev, “On alternative approximating distributions in the multivariate version of Kolmogorov's second uniform limit theorem”, Teor. Veroyatnost. i Primenen., 67:1 (2022), 3–22; Theory Probab. Appl., 67:1 (2022), 1–16
Citation in format AMSBIB
\Bibitem{GotZai22}
\by F.~G\"otze, A.~Yu.~Zaitsev
\paper On alternative approximating distributions in the multivariate version of Kolmogorov's second uniform limit theorem
\jour Teor. Veroyatnost. i Primenen.
\yr 2022
\vol 67
\issue 1
\pages 3--22
\mathnet{http://mi.mathnet.ru/tvp5416}
\crossref{https://doi.org/10.4213/tvp5416}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4466409}
\zmath{https://zbmath.org/?q=an:7523555}
\transl
\jour Theory Probab. Appl.
\yr 2022
\vol 67
\issue 1
\pages 1--16
\crossref{https://doi.org/10.1137/S0040585X97T99071X}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85131042694}
Linking options:
  • https://www.mathnet.ru/eng/tvp5416
  • https://doi.org/10.4213/tvp5416
  • https://www.mathnet.ru/eng/tvp/v67/i1/p3
    • This publication is cited in the following 2 articles:
    1. F. Götze, A. Yu. Zaitsev, “Convergence to infinite-dimensional compound Poisson distributions on convex polyhedra”, J. Math. Sci., 273:5 (2023), 732–737  crossref  mathscinet
    2. V. {\v , Y. Novak, “Compound Poisson approximation”, Probab. Surveys, 19:none (2022)  crossref  mathscinet  zmath
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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