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Accuracy of approximation in the Poisson theorem in terms of the χ2-distance

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Abstract

We study the limit behavior of the χ2-distance between the distributions of the nth partial sum of independent not necessarily identically distributed Bernoulli random variables and the accompanying Poisson law. As a consequence in the i.i.d. case we make the multiplicative constant preciser in the available upper bound for the rate of convergence in the Poisson limit theorem.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Novosibirsk, Russia

    I. S. Borisov

  2. Novosibirsk State University, Novosibirsk, Russia

    I. S. Vorozheikin

Authors
  1. I. S. Borisov
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  2. I. S. Vorozheikin
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Corresponding author

Correspondence to I. S. Borisov.

Additional information

Original Russian Text Copyright © 2008 Borisov I. S. and Vorozheĭkin I. S.

The authors were partially supported by the Russian Foundation for Basic Research (Grants 05-01-00810 and 06-01-00738) and INTAS (Grant 03-51-5018).

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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 49, No. 1, pp. 8–22, January–February, 2008.

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Borisov, I.S., Vorozheikin, I.S. Accuracy of approximation in the Poisson theorem in terms of the χ2-distance. Sib Math J 49, 5–17 (2008). https://doi.org/10.1007/s11202-008-0002-3

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  • DOI: https://doi.org/10.1007/s11202-008-0002-3

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