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Teor. Veroyatnost. i Primenen., 2003, Volume 48, Issue 3, Pages 576–583 (Mi tvp271)  

This article is cited in 2 scientific papers (total in 2 papers)

Short Communications

A note on Dobrushin's theorem and couplings in poisson approximation in abelian groups

I. S. Borisov

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences

Abstract: A more general version of Dobrushin's result connected with an optimal coupling of two random variables is proven. An application to the problem of Poisson approximation in Abelian groups is considered. In particular, an optimal coupling in Poisson approximation of empirical processes is studied.

Keywords: Monge–Kantorovich problem, duality theorem, Abelian group, empirical process, empirical measure, Poisson point process, Poisson approximation, coupling.

DOI: https://doi.org/10.4213/tvp271

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English version:
Theory of Probability and its Applications, 2004, 48:3, 521–528

Bibliographic databases:

Received: 16.12.2002

Citation: I. S. Borisov, “A note on Dobrushin's theorem and couplings in poisson approximation in abelian groups”, Teor. Veroyatnost. i Primenen., 48:3 (2003), 576–583; Theory Probab. Appl., 48:3 (2004), 521–528

Citation in format AMSBIB
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\by I.~S.~Borisov
\paper A note on Dobrushin's theorem and couplings in
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\pages 576--583
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\transl
\jour Theory Probab. Appl.
\yr 2004
\vol 48
\issue 3
\pages 521--528
\crossref{https://doi.org/10.1137/S0040585X97980579}
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. I. S. Borisov, A. M. Shoisoronov, “A continuity theorem in the ruin problem”, Siberian Math. J., 52:4 (2011), 602–611  mathnet  crossref  mathscinet  isi
    2. Roos B., “Refined Total Variation Bounds in the Multivariate and Compound Poisson Approximation”, ALEA-Latin Am. J. Probab. Math. Stat., 14:1 (2017), 337–360  mathscinet  zmath  isi
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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