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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2013, Volume 282, Pages 165–180
DOI: https://doi.org/10.1134/S037196851303014X (Mi tm3497) 		 
This article is cited in 6 scientific papers (total in 6 papers)

Estimate for the accuracy of the Poisson approximation for the number of empty cells in an equiprobable scheme for group allocation of particles, and applications

V. G. Mikhailov

Steklov Mathematical Institute of the Russian Academy of Sciences, Moscow, Russia
Full-text PDF (227 kB) Citations (6)
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DOI: https://doi.org/10.1134/S037196851303014X
Abstract: The properties of the distribution of the number of empty cells are analyzed for a natural generalization of an equiprobable scheme for group allocation of particles. An error estimate is obtained for the Chen–Stein method of Poisson approximation for the distribution of the number of empty cells in this scheme. This estimate is used to derive sufficient conditions for the distribution of the number of empty cells to converge to the convolutions of the Poisson distribution and two-point distributions. On the basis of these results, asymptotic properties of the solution set of a perturbed system of linear Boolean equations are studied (in the case of consistent increase in the number of unknowns and the number of equations).
Received in December 2012
English version:
Proceedings of the Steklov Institute of Mathematics, 2013, Volume 282, Pages 157–171
DOI: https://doi.org/10.1134/S008154381306014X
Bibliographic databases:
Document Type: Article
UDC: 519.212.2
Language: Russian
Citation: V. G. Mikhailov, “Estimate for the accuracy of the Poisson approximation for the number of empty cells in an equiprobable scheme for group allocation of particles, and applications”, Branching processes, random walks, and related problems, Collected papers. Dedicated to the memory of Boris Aleksandrovich Sevastyanov, corresponding member of the Russian Academy of Sciences, Trudy Mat. Inst. Steklova, 282, MAIK Nauka/Interperiodica, Moscow, 2013, 165–180; Proc. Steklov Inst. Math., 282 (2013), 157–171
Citation in format AMSBIB
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\inbook Branching processes, random walks, and related problems
\bookinfo Collected papers. Dedicated to the memory of Boris Aleksandrovich Sevastyanov, corresponding member of the Russian Academy of Sciences
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\vol 282
\pages 165--180
\publ MAIK Nauka/Interperiodica
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    • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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