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Teor. Veroyatnost. i Primenen., 1958, Volume 3, Issue 2, Pages 153–165 (Mi tvp4926)  

This article is cited in 2 scientific papers (total in 2 papers)

Strong Stability of Sums and Infinitely Divisible Distributions

Yu. V. Prokhorov

Moscow

Abstract: The paper gives some new conditions for the strong law of large numbers (s. 1. 1. n.) to be applied to a sequence of independent symmetrical random variables (r. v.).
The principal result states that the s.1.1. n. for a sequence of “adjoined” infinitely divisible r. v. implies the s. 1. 1. n. for the given sequence of r. v.
This result leads to “satisfactory” sufficient conditions for s. l. l. n. In special cases some of these conditions become the necessary ones.

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English version:
Theory of Probability and its Applications, 1958, 4:2, 141–153

Received: 15.02.1958

Citation: Yu. V. Prokhorov, “Strong Stability of Sums and Infinitely Divisible Distributions”, Teor. Veroyatnost. i Primenen., 3:2 (1958), 153–165; Theory Probab. Appl., 4:2 (1958), 141–153

Citation in format AMSBIB
\Bibitem{Pro58}
\by Yu.~V.~Prokhorov
\paper Strong Stability of Sums and Infinitely Divisible Distributions
\jour Teor. Veroyatnost. i Primenen.
\yr 1958
\vol 3
\issue 2
\pages 153--165
\mathnet{http://mi.mathnet.ru/tvp4926}
\transl
\jour Theory Probab. Appl.
\yr 1958
\vol 4
\issue 2
\pages 141--153
\crossref{https://doi.org/10.1137/1103013}


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    Erratum

    This publication is cited in the following articles:
    1. S. V. Astashkin, F. A. Sukochev, “Series of independent mean zero random variables in rearrangement invariant spaces with the Kruglov property”, J. Math. Sci. (N. Y.), 148:6 (2008), 795–809  mathnet  crossref  mathscinet  elib  elib
    2. S. V. Astashkin, F. A. Sukochev, “Independent functions and the geometry of Banach spaces”, Russian Math. Surveys, 65:6 (2010), 1003–1081  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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