An Arithmetic Method for Obtaining Local Limit Theorems for Lattice Random Variables

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Previous article Next article An Arithmetic Method for Obtaining Local Limit Theorems for Lattice Random VariablesD. A. Moskvin, L. P. Postnikova, and A. A. YudinD. A. Moskvin, L. P. Postnikova, and A. A. Yudinhttps://doi.org/10.1137/1115006PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] I. A. Ibragimov and , Yu. V. Linnik, Independent Stationarily Connected Random Variables, Izd-vo “Nauka”, Moscow, 1965, (In Russian.) Google Scholar[2] N. G. Gamkrelidze, On the local limit theorem for lattice random variables, Theory Prob. Applications, 9 (1964), 662–664 10.1137/1109091 0141.16406 LinkGoogle Scholar[3] N. G. Gamkrelidze, A certain lower estimate for the speed of convergence in the local theorem, Litovsk. Mat. Sb., 7 (1967), 405–408 (1968), (In Russian.) MR0228047 Google Scholar[4] N. G. Gamkrelidze, On the connection between the local and integral theorems for lattice distributions, Theory Prob. Applications, 13 (1968), 174–179 10.1137/1113017 0196.20603 LinkGoogle Scholar[5] A. A. Mitalauskas and , V. A. Statuljavičjus, Local limit theorems and asymptotic expansions for sums of independent lattice random variables, Litovsk. Mat. Sb., 6 (1966), 569–583 MR0214116 Google Scholar[6] G. A. Freyman, Elements of the Structural Theory of Set Summation, Kazan', 1966, (In Russian.) Google Scholar[7] L. P. Postnikova, Fluctuations in the distribution of fractional parts, Dokl. Akad. Nauk SSSR, 161 (1965), 1282–1284, (In Russian.) MR0181629 Google Scholar[8] G. A. Freyman, An elementary method for proving limit theorems in probability theory, Vestnik Leningrad. Univ., 1 (1956), 57–73, (In Russian.) Google Scholar[9] G. A. Freyman, Waring's problem with increasing number of terms, Uchenye Zapiski Elabuzhsk. Ped. Inst., 3 (1958), 115–119, (In Russian.) Google Scholar[10] I. V. Vinogradov, Foundations of Number Theory, Izd-vo “Nauka”, Moscow, 1965, (In Russian.) Google Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails On the measure of large values of the modulus of a trigonometric sumEuropean Journal of Combinatorics, Vol. 34, No. 8 | 1 Nov 2013 Cross Ref Distribution of the sizes of two dimensional lattice animals as a function of perimeter or energyZeitschrift f�r Physik B Condensed Matter and Quanta, Vol. 33, No. 1 | 1 Mar 1979 Cross Ref Structure Theory of Set Addition and Local Limit Theorems for Independent Lattice Random VariablesTheory of Probability & Its Applications, Vol. 19, No. 1 | 28 July 2006AbstractPDF (732 KB)A Local Limit Theorem for Large Deviations in the Case of Differently Distributed Lattice SummandsTheory of Probability & Its Applications, Vol. 17, No. 4 | 28 July 2006AbstractPDF (441 KB)Central and local limit theorems applied to asymptotic enumerationJournal of Combinatorial Theory, Series A, Vol. 15, No. 1 | 1 Jul 1973 Cross Ref Volume 15, Issue 1| 1970Theory of Probability & Its Applications History Submitted:10 December 1969Published online:17 July 2006 InformationCopyright © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1115006Article page range:pp. 87-97ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics