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An invariance principle and some convergence rate results for branching processes. (English) Zbl 0212.49505

MSC:
60J80 Branching processes (Galton-Watson, birth-and-death, etc.)
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[1] Billingsley, P.: Convergence of probability measures. New York: Wiley 1968. · Zbl 0172.21201
[2] Bühler, W. J.: Ein zentraler Grenzwertsatz für Verzweigungsprozesse. Z. Wahrscheinlichkeitstheorie verw. Geb. 11, 139-141 (1969). · Zbl 0165.19403 · doi:10.1007/BF00531814
[3] Harris, T.E.: The theory of branching processes. Berlin-Göttingen-Heidelberg: Springer 1963. · Zbl 0117.13002
[4] Heyde, C.C.: Some central limit analogues for super-critical Galton-Watson processes. J. appl. Probab. 8, 52-59 (1971). · Zbl 0222.60054 · doi:10.2307/3211837
[5] Ibragimov, I.A.: On the accuracy of the Gaussian approximation to the distribution function of sums of independent variables. Theor. Probab. Appl. 11, 559-579 (1966). · Zbl 0161.15207 · doi:10.1137/1111061
[6] Zolotarev, V.M.: A sharpening of the inequality of Berry-Esseen. Z. Wahrscheinlichkeitstheorie verw. Geb. 8, 332-342 (1967). · Zbl 0157.25501 · doi:10.1007/BF00531598
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