Abstract:
We consider the analogue of the first uniform Kolmogorov theorem in the scheme of series. Zaitsev's hypothesis on accuracy of approximation is partially confirmed. As approximations we use compound Poisson approximations and compound Poisson measures with a sign.
Citation:
V. Čekanavičius, “On compound Poisson approximations under moment restrictions”, Teor. Veroyatnost. i Primenen., 44:1 (1999), 74–86; Theory Probab. Appl., 44:1 (2000), 18–28
\Bibitem{Cek99}
\by V.~{\v C}ekanavi{\v{c}}ius
\paper On compound Poisson approximations under moment restrictions
\jour Teor. Veroyatnost. i Primenen.
\yr 1999
\vol 44
\issue 1
\pages 74--86
\mathnet{http://mi.mathnet.ru/tvp598}
\crossref{https://doi.org/10.4213/tvp598}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1751189}
\zmath{https://zbmath.org/?q=an:0958.60010}
\transl
\jour Theory Probab. Appl.
\yr 2000
\vol 44
\issue 1
\pages 18--28
\crossref{https://doi.org/10.1137/S0040585X97977343}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000087555000002}
Linking options:
https://www.mathnet.ru/eng/tvp598
https://doi.org/10.4213/tvp598
https://www.mathnet.ru/eng/tvp/v44/i1/p74
This publication is cited in the following 8 articles:
S. Y. Novak, “On Poisson Approximation”, J Theor Probab, 2024
Ya. S. Golikova, A. Yu. Zaitsev, “O tochnosti bezgranichno delimoi approksimatsii n-kratnykh svertok veroyatnostnykh raspredelenii”, Veroyatnost i statistika. 33, Zap. nauchn. sem. POMI, 515, POMI, SPb., 2022, 83–90
V. Čekanavičius, S. Y. Novak, “Compound Poisson approximation”, Probab. Surveys, 19:none (2022)
M. A. Lifshits, Ya. Yu. Nikitin, V. V. Petrov, A. Yu. Zaitsev, A. A. Zinger, “Toward the history of the Saint Petersburg school of probability and statistics. I. Limit theorems for sums of independent random variables”, Vestn. St Petersb. Univ. Math., 51:2 (2018), 144–163
Cekanavicius V., “Approximation Methods in Probability Theory”, Approximation Methods in Probability Theory, Universitext, Springer International Publishing Ag, 2016, 1–274
Pavel Samusenko, Nonparametric criteria for sparse contingency tables, 2012
D. N. Karymov, “On the decomposition of lattice distributions
into convolutions of Poisson signed measures”, Theory Probab. Appl., 49:3 (2005), 545–552
Cekanavicius V., “Infinitely divisible approximations for discrete nonlattice variables”, Advances in Applied Probability, 35:4 (2003), 982–1006
Citation in format AMSBIB
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