General Theorems on the Factorization of Infinitely Divisible Laws III. Sufficient Conditions (Countable Bounded Poisson Spectrum. Unbounded Spectrum. “Stability”)

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Previous article Next article General Theorems on the Factorization of Infinitely Divisible Laws III. Sufficient Conditions (Countable Bounded Poisson Spectrum. Unbounded Spectrum. “Stability”)Yu. V. LinnikYu. V. Linnikhttps://doi.org/10.1137/1104013PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAboutAbstractThe case of a countable bounded Poisson spectrum is considered. Some cases of the unbounded spectrum (with small high frequency energy) are treated.[1] Yu. V. Linnik, General theorems on the factorization of infinitely divisible laws, Theory Prob. Applications, 3 (1958), , I, (Translation from the Russian, this journal.) 0094.32504 LinkGoogle Scholar[2] Yu. V. Linnik, General theorems on the factorization of infinitely divisible laws. II. Sufficient conditions (case of a finite Poisson spectrum), Theor. Probability Appl., 4 (1959), 53–82, (Translation from the Russian, this journal.) 10.1137/1104002 MR0121851 LinkGoogle Scholar[3] Yu. V. Linnik, On the decomposition of the composition of Gaussian and Poisson laws, Theory Prob. Applications, 2 (1957), , (Translation from the Russian, this journal.) LinkGoogle Scholar[4] E. S. Titchmarsh, Introduction to the Theory of Fourier Integrals, Oxford University Press, 1937 0017.40404 Google Scholar[5] E. Phragmen, Sur une extension d'une théorème classique de la théor ie des fonctions, Acta Math., 28 (1904), 351–368 CrossrefGoogle Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Regularized distributions and entropic stability of Cramer’s characterization of the normal lawStochastic Processes and their Applications, Vol. 126, No. 12 Cross Ref Chapter 15 Entropic instability of Cramer’s characterization of the normal law2 November 2011 Cross Ref The Exact-Order Estimates of Decompositional Stability of Linnik’s $\mathfrak{L}$ Class DistributionsG. P. Chistyakov28 July 2006 | Theory of Probability & Its Applications, Vol. 39, No. 2AbstractPDF (833 KB)Decompositional Stability of Distribution LawsG. P. Chistyakov28 July 2006 | Theory of Probability & Its Applications, Vol. 31, No. 3AbstractPDF (1807 KB)Decomposition of the Convolution of Two Poisson Distributions on a Locally Compact Abelian GroupG. M. Fel’dman and A. E. Fryntov17 July 2006 | Theory of Probability & Its Applications, Vol. 26, No. 3AbstractPDF (668 KB)Yu. V. Linnik’S Work in Probability Theory and Mathematical Statistics17 July 2006 | Theory of Probability & Its Applications, Vol. 10, No. 1AbstractPDF (1735 KB) Volume 4, Issue 2| 1959Theory of Probability & Its Applications History Submitted:31 October 1957Published online:17 July 2006 InformationCopyright © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1104013Article page range:pp. 142-163ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics