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 Teor. Veroyatnost. i Primenen.: Year: Volume: Issue: Page: Find

 Teor. Veroyatnost. i Primenen., 1965, Volume 10, Issue 4, Pages 645–659 (Mi tvp565)

Limit theorems for the density functions and asymptotic expansions for the distributions of sums of independent random variables

V. A. Statulevichius

Vilnius

Abstract: Limit theorems for the density functions (theorems 1–3) and asymptotic expansions for the distribution functions and the density functions (theorems 4–5) of sums of nonidentically distributed independent random variables are given.

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English version:
Theory of Probability and its Applications, 1965, 10:4, 582–595

Bibliographic databases:

Citation: V. A. Statulevichius, “Limit theorems for the density functions and asymptotic expansions for the distributions of sums of independent random variables”, Teor. Veroyatnost. i Primenen., 10:4 (1965), 645–659; Theory Probab. Appl., 10:4 (1965), 582–595

Citation in format AMSBIB
\Bibitem{Sta65} \by V.~A.~Statulevichius \paper Limit theorems for the density functions and asymptotic expansions for the distributions of sums of independent random variables \jour Teor. Veroyatnost. i Primenen. \yr 1965 \vol 10 \issue 4 \pages 645--659 \mathnet{http://mi.mathnet.ru/tvp565} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=193660} \zmath{https://zbmath.org/?q=an:0178.53803} \transl \jour Theory Probab. Appl. \yr 1965 \vol 10 \issue 4 \pages 582--595 \crossref{https://doi.org/10.1137/1110074} 

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Citing articles on Google Scholar: Russian citations, English citations
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This publication is cited in the following articles:
1. S. B. Shlosman, “Absence of continuous symmetry breaking in two-dimensional models of statistical physics”, Theoret. and Math. Phys., 33:1 (1977), 897–902
2. L. V. Rozovskii, “Superlarge deviations of a sum of independent random variables having a common absolutely continuous distribution under the Cramér condition”, Theory Probab. Appl., 48:1 (2004), 108–130
3. A. Yu. Veretennikov, S. A. Klokov, “On local mixing conditions for SDE approximations”, Theory Probab. Appl., 57:1 (2013), 110–131
4. Cekanavicius V., “Approximation Methods in Probability Theory”, Approximation Methods in Probability Theory, Universitext, Springer International Publishing Ag, 2016, 1–274
5. Bobkov S.G., “Asymptotic Expansions For Products of Characteristic Functions Under Moment Assumptions of Non-Integer Orders”, Convexity and Concentration, IMA Volumes in Mathematics and Its Applications, 161, ed. Carlen E. Madiman M. Werner E., Springer, 2017, 297–357
6. Bobkov S.G., “Berry-Esseen Bounds and Edgeworth Expansions in the Central Limit Theorem For Transport Distances”, Probab. Theory Relat. Field, 170:1-2 (2018), 229–262