The Convergence of Moments in a Random Limit Theorem of H. Robbins’ Type
1989; Society for Industrial and Applied Mathematics; Volume: 33; Issue: 1 Linguagem: Inglês
10.1137/1133007
ISSN1095-7219
AutoresK. S. Kubacki, Dominik Szynal,
Tópico(s)advanced mathematical theories
ResumoPrevious article Next article The Convergence of Moments in a Random Limit Theorem of H. Robbins’ TypeK. S. Kubacki and D. SzynalK. S. Kubacki and D. Szynalhttps://doi.org/10.1137/1133007PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] S. N. Bernstein, Some remarks concerning the limit theorem of Liapunov, Doklady Akad. Nauk SSSR (N.S.), 24 (1939), 3–7, (In Russian.) 1,340h Google Scholar[2] Patrick Billingsley, Convergence of probability measures, John Wiley & Sons Inc., New York, 1968xii+253 38:1718 0172.21201 Google Scholar[3] Bruce M. Brown, Moments of a stopping rule related to the central limit theorem, Ann. Math. Statist., 40 (1969), 1236–1249 39:5010 0212.21103 CrossrefGoogle Scholar[4] B. M. Brown, Characteristic functions, moments, and the central limit theorem, Ann. Math. Statist., 41 (1970), 658–664 41:6285 0196.21204 CrossrefGoogle Scholar[5] D. L. Burkholder, Distribution function inequalities for martingales, Ann. Probability, 1 (1973), 19–42 51:1944 0301.60035 CrossrefGoogle Scholar[6] Peter Hall, The convergence of moments in the martingale central limit theorem, Z. Wahrsch. Verw. Gebiete, 44 (1978), 253–260 58:24474 0369.60026 CrossrefGoogle Scholar[7] V. M, Kruglov, Convergence of numerical characteristics of independent random variables with values in a Hilbert space, Theory Probab. Appl., 18 (1973), 694–712 10.1137/1118091 0321.60045 LinkGoogle Scholar[8] V. M. Lifshits, On the convergence of moments in the central limit theorem for non-homogeneous Markov chains, Theory Probab. Appl., 4 (1975), 741–758 Google Scholar[9] M. N. Marushin and , V. P. Krivorukov, Some remarks on the central limit theorem of the theory of moments of even order for sums of random number of independent identically distributed random variables, Ukrainian Math. J., 36 (1984), 18–24 0561.60028 CrossrefGoogle Scholar[10] Jacques Neveu, Mathematical foundations of the calculus of probability, Translated by Amiel Feinstein, Holden-Day Inc., San Francisco, Calif., 1965xiii+223 33:6660 0137.11301 Google Scholar[11] Herbert Robbins, The asymptotic distribution of the sum of a random number of random variables, Bull. Amer. Math. Soc., 54 (1948), 1151–1161 10,385a 0034.22503 CrossrefGoogle Scholar[12] Z. Rychlik and , D. Szynal, On the limit behaviour of sums of a random number of independent random variables, Colloq. Math., 28 (1973), 147–159 48:12630 0238.60015 CrossrefGoogle Scholar[13] Z. Rychlik and , D. Szynal, On the rate of approximation in the random-sum central limit theorem, Theory Probab. Appl., 24 (1979), 614–620 Google Scholar[14] A. N. Shiryaev, Probability, Graduate Texts in Mathematics, Vol. 95, Springer-Verlag, New York, 1984xi+577, Berlin, Heidelberg 85a:60007 0536.60001 CrossrefGoogle Scholar[15] S. K. Zaremba, Note on the central limit theorem, Math. Z., 69 (1958), 295–298 20:5516 0081.35201 CrossrefGoogle Scholar[16] Vladimir M. Zolotarev, Théorèmes limites pour les sommes de variables aléatoires indépendantes qui ne sont pas infinitésimales, C. R. Acad. Sci. Paris Sér. A-B, 264 (1967), A799–A800 36:7187 0153.19503 Google Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails Modeling Particle Size Distribution in Lunar Regolith via a Central Limit Theorem for Random SumsMathematics, Vol. 8, No. 9 | 23 August 2020 Cross Ref On the Convergence of Moments in a Martingale Central Limit TheoremK. S. KubackiTheory of Probability & Its Applications, Vol. 40, No. 2 | 12 July 2006AbstractPDF (1101 KB)On Limit Distributions of Randomly Indexed Random SequencesV. Yu. KorolevTheory of Probability & Its Applications, Vol. 37, No. 3 | 17 July 2006AbstractPDF (893 KB)The Convergence of Moments of Random SumsV. M. KruglovTheory of Probability & Its Applications, Vol. 33, No. 2 | 17 July 2006AbstractPDF (419 KB) Volume 33, Issue 1| 1989Theory of Probability & Its Applications1-205 History Submitted:21 April 1986Published online:17 July 2006 InformationCopyright © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1133007Article page range:pp. 75-85ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics
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