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Teoriya Veroyatnostei i ee Primeneniya, 1994, Volume 39, Issue 2, Pages 248–271 (Mi tvp3801)  
Convergence of convolutions of concentration functions to degenerate, normal, and Poisson laws

Sh. O. Alekperov, V. M. Kruglova

a M. V. Lomonosov Moscow State University, Faculty of Computational Mathematics and Cybernetics
Full-text PDF (1066 kB)
Abstract: The paper compares the behavior of convolutions of distribution functions and that of convolutions of corresponding concentration functions. It is shown that the weak convergence of a sequence of convolutions of distribution functions is equivalent to the weak convergence of a sequence of convolutions of corresponding concentration functions to normal, Poisson, and degenerate laws. The most of statements are supposed to be uniform, inside the convolution, closeness of the concentration components to degenerate laws.
Keywords: concentration function, distribution function, weak convergence, random variable.
Received: 24.08.1993
English version:
Theory of Probability and its Applications, 1994, Volume 39, Issue 2, Pages 197–216
DOI: https://doi.org/10.1137/1139012
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: Sh. O. Alekperov, V. M. Kruglov, “Convergence of convolutions of concentration functions to degenerate, normal, and Poisson laws”, Teor. Veroyatnost. i Primenen., 39:2 (1994), 248–271; Theory Probab. Appl., 39:2 (1994), 197–216
Citation in format AMSBIB
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\paper Convergence of convolutions of concentration functions to degenerate, normal, and Poisson laws
\jour Teor. Veroyatnost. i Primenen.
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\vol 39
\issue 2
\pages 248--271
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\transl
\jour Theory Probab. Appl.
\yr 1994
\vol 39
\issue 2
\pages 197--216
\crossref{https://doi.org/10.1137/1139012}
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