A Limit Theorem for Random Sums of Dependent Indicators and Its Applications in the Theory of Branching Processes

Previous article Next article A Limit Theorem for Random Sums of Dependent Indicators and Its Applications in the Theory of Branching ProcessesI. RakhimovI. Rakhimovhttps://doi.org/10.1137/1132038PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] B. A. Sevast'yanov, Poisson limit law in the scheme of sums of dependent random variables, Theory Probab. Appl., 17 (1972), 695–699 10.1137/1117082 0299.60024 LinkGoogle Scholar[2] A. S. Ambrosimov, Normal law in the scheme of sums of dependent random variables considered by B. A. Sevast'yanov, Theory Probab. Appl., 21 (1976), 183–188 10.1137/1121020 LinkGoogle Scholar[3] A. M. Zubkov, Inequalities for the distribution of a sum of functions of independent random variables, Mat. Zametki, 22 (1977), 745–758, (In Russian.) 57:10780 Google Scholar[4] A. M. Zubkov and , V. G. Mikhailov, Estimate of the accuracy of Poisson approximation in the problem of allocation of particles in cells, Theory Probab. Appl., 23 (1978), 789–794 10.1137/1123094 0422.60005 LinkGoogle Scholar[5] Bernard Silverman and , Tim Brown, Short distances, flat triangles and Poisson limits, J. Appl. Probab., 15 (1978), 815–825 80c:60042 0396.60029 CrossrefGoogle Scholar[6] A. D. Barbour and , G. K. Eagleson, Poisson approximation for some statistics based on exchangeable trials, Adv. in Appl. Probab., 15 (1983), 585–600 85c:60021 0511.60025 CrossrefGoogle Scholar[7] Klaus Fleischmann and , Rainer Siegmund-Schultze, The structure of reduced critical Galton-Watson processes, Math. Nachr., 79 (1977), 233–241 57:1674 0299.60065 CrossrefGoogle Scholar[8] A. L. Yakymiv, Asymptotic properties of subcritical and supercritical reduced branching processes, Theory Probab. Appl., 30 (1985), 201–207 10.1137/1130027 0657.60105 LinkGoogle Scholar[9] B. A. Sevast'yanov, Verzweigungsprozesse, Akademie-Verlag, Berlin, 1974xi+326 53:11785 Google Scholar[10] Krishna B. Athreya and , Peter E. Ney, Branching processes, Springer-Verlag, New York, 1972xi+287 51:9242 0259.60002 CrossrefGoogle Scholar[11] Krishna B. Athreya and , Peter Ney, The local limit theorem and some related aspects of super-critical branching processes, Trans. Amer. Math. Soc., 152 (1970), 233–251 42:3868 0214.16203 CrossrefGoogle Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Branching Processes as Sums of Dependent Random Variables Cross Ref Estimates for the Convergence Rate to the Poisson Distribution for Random Sums of Independent IndicatorsP. L. Logunov17 July 2006 | Theory of Probability & Its Applications, Vol. 35, No. 3AbstractPDF (324 KB) Volume 32, Issue 2| 1988Theory of Probability & Its Applications History Submitted:10 October 1985Published online:17 July 2006 InformationCopyright © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1132038Article page range:pp. 290-298ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics

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