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Mat. Sb. (N.S.), 1974, Volume 94(136), Number 2(6), Pages 283–299 (Mi msb3682)  

This article is cited in 4 scientific papers (total in 4 papers)

Convergence to a process with independent increments in a scheme of increasing sums of dependent random variables

V. G. Mikhailov


Abstract: This article derives conditions under which a sequence of random set functions on subsets of a finite-dimensional space constructed in terms of increasing sums of dependent nonnegative random variables converges (in the sense of convergence of finite-dimensional distributions) to a random set function with independent increments which have infinitely divisible distributions. The results obtained are applied to the problem of the number of long repetitions in a sequence of trials.
Bibliography: 4 titles.

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English version:
Mathematics of the USSR-Sbornik, 1974, 23:2, 271–286

Bibliographic databases:

UDC: 519.2
MSC: Primary 60F05; Secondary 60J30
Received: 20.11.1973

Citation: V. G. Mikhailov, “Convergence to a process with independent increments in a scheme of increasing sums of dependent random variables”, Mat. Sb. (N.S.), 94(136):2(6) (1974), 283–299; Math. USSR-Sb., 23:2 (1974), 271–286

Citation in format AMSBIB
\Bibitem{Mik74}
\by V.~G.~Mikhailov
\paper Convergence to a~process with independent increments in a~scheme of increasing sums of dependent random variables
\jour Mat. Sb. (N.S.)
\yr 1974
\vol 94(136)
\issue 2(6)
\pages 283--299
\mathnet{http://mi.mathnet.ru/msb3682}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=356181}
\zmath{https://zbmath.org/?q=an:0324.60023}
\transl
\jour Math. USSR-Sb.
\yr 1974
\vol 23
\issue 2
\pages 271--286
\crossref{https://doi.org/10.1070/SM1974v023n02ABEH001720}


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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. Levashov M., “Limit-Theorems of the Poisson Type for Inhomogeneous U-Statistics”, no. 3, 1990, 12–14  isi
    2. V. G. Mikhailov, “Limit theorems for the number of points of a given set covered by a random linear subspace”, Discrete Math. Appl., 13:2 (2003), 179–188  mathnet  crossref  crossref  mathscinet  zmath
    3. V. A. Kopyttsev, “A multivariate Poisson theorem for the number of solutions close to given vectors of a system of random linear equations”, Discrete Math. Appl., 17:6 (2007), 567–586  mathnet  crossref  crossref  mathscinet  zmath  elib
    4. V. A. Kopyttsev, “Mnogomernaya teorema Puassona dlya chisel reshenii sluchainykh vklyuchenii, blizkikh k zadannym vektoram”, Matem. vopr. kriptogr., 7:4 (2016), 67–80  mathnet  crossref  mathscinet  elib
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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