Uniqueness of Symmetric Distribution Functions Defined on Bounded Sets and Its Applications
Gerhard Siegel · Theory of Probability and Its Applications · 1980
Previous article Next article Uniqueness of Symmetric Distribution Functions Defined on Bounded Sets and Its ApplicationsG. SiegelG. Siegelhttps://doi.org/10.1137/1124096PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] B. V. Gnedenko and , A. N. Kolmogorov, Limit distributions for sums of independent random variables, Addison-Wesley Publishing Company, Inc., Cambridge, Mass., 1954ix+264 MR0062975 0056.36001 Google Scholar[2] I. A. Ibragimov and , Yu. V. Linnik, Independent and stationary sequences of random variables, Wolters-Noordhoff Publishing, Groningen, 1971, 443– MR0322926 0219.60027 Google Scholar[3] I. A. Ibragimov, On determining an infinitely divisible distribution function by its values on a half-line, Theory Prob. Applications, 22 (1971), 384–390 10.1137/1122043 0379.60018 LinkGoogle Scholar[4] B. Jesiak, On analytic distribution functions and analytic properties of infinitely divisible functions, Theory Prob. Applications, 24 (1979), 824–830, (this issue) 10.1137/1124095 0432.60018 LinkGoogle Scholar[5] H.-J. Rossberg and , B. Jesiak, On the unique determination of stable distribution functions, Math. Nachr., 82 (1978), 297–308 MR0488223 0326.60012 CrossrefGoogle Scholar[6] Tatsuo Kawata, Fourier analysis in probability theory, Academic Press, New York, 1972xii+668 MR0464353 0271.60022 Google Scholar[7] Yu. V. Linnik, Decompositions of Probability Distributions, Oliver & Boyd, Edinburgh, 1973 Google Scholar[8] H.-J. Rossberg, On a problem of Kolmogorov concerning the normal distribution, Theory Prob. Applications, 19 (1976), 795–798 10.1137/1119085 0323.60026 LinkGoogle Scholar[9] H.-J. Rossberg and , G. Siegel, Continuation of convergence in the central limit theorem, Theory Prob. Applications, 20 (1975), 866–868 10.1137/1120095 0362.60042 LinkGoogle Scholar[10] G. Siegel, Zero-one laws and weak convergences for sums of independent random variables, Math. Nachr., 86 (1978), 333–346 MR532790 0406.60026 CrossrefGoogle Scholar[11] H.-J. Rossberg and , B. Jesiak, On the unique determination of stable distribution functions, Math. Nachr., 82 (1978), 297–308, (In Russian.) MR0488223 0326.60012 CrossrefGoogle Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails Limit Theorems Involving Restricted ConvergenceTheory of Probability & Its Applications, Vol. 39, No. 2 | 28 July 2006AbstractPDF (2035 KB)On Uniqueness Conditions for Functions of Bounded Variation and Distribution Functions with Values on the Half-LineTheory of Probability & Its Applications, Vol. 27, No. 4 | 17 July 2006AbstractPDF (329 KB)One-Sided Characterization of the Normal Distribution in the Set of Infinitely Divisible DistributionsTheory of Probability & Its Applications, Vol. 26, No. 2 | 17 July 2006AbstractPDF (665 KB)On Analytic Distribution Functions and Analytic Properties of Infinitely Divisible Distribution FunctionsTheory of Probability & Its Applications, Vol. 24, No. 4 | 17 July 2006AbstractPDF (610 KB)Limit Theorems for Identically Distributed Summands Asuming the Convergence of the Distribution Functions on a Half AxisTheory of Probability & Its Applications, Vol. 24, No. 4 | 17 July 2006AbstractPDF (1398 KB) Volume 24, Issue 4| 1980Theory of Probability & Its Applications675-896 History Submitted:17 January 1977Published online:17 July 2006 InformationCopyright © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1124096Article page range:pp. 830-833ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics