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Almost sure behavior of linear functionals of supercritical branching processes. (English) Zbl 0376.60083

MSC:
60J80 Branching processes (Galton-Watson, birth-and-death, etc.)
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[1] Søren Asmussen, Convergence rates for branching processes, Ann. Probability 4 (1976), no. 1, 139 – 146. · Zbl 0329.60053
[2] Søren Asmussen and Heinrich Hering, Strong limit theorems for general supercritical branching processes with applications to branching diffusions, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 36 (1976), no. 3, 195 – 212. · Zbl 0325.60081 · doi:10.1007/BF00532545 · doi.org
[3] Krishna Balasundaram Athreya, Limit theorems for multitype continuous time Markov branching processes. I. The case of an eigenvector linear functional, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 12 (1969), 320 – 332. · Zbl 0181.21101 · doi:10.1007/BF00538753 · doi.org
[4] Krishna Balasundaram Athreya, Limit theorems for multitype continuous time Markov branching processes. II. The case of an arbitrary linear functional, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 13 (1969), 204 – 214. · Zbl 0181.21102 · doi:10.1007/BF00539201 · doi.org
[5] Krishna B. Athreya, Some refinements in the theory of supercritical multitype Markov branching processes, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 20 (1971), 47 – 57. · Zbl 0209.19304 · doi:10.1007/BF00534165 · doi.org
[6] Krishna B. Athreya and Peter E. Ney, Branching processes, Springer-Verlag, New York-Heidelberg, 1972. Die Grundlehren der mathematischen Wissenschaften, Band 196. · Zbl 1070.60001
[7] Andrew D. Barbour, Tail sums of convergent series of independent random variables, Proc. Cambridge Philos. Soc. 75 (1974), 361 – 364. · Zbl 0279.60033
[8] Y. S. Chow and H. Teicher, Iterated logarithm laws for weighted averages, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 26 (1973), 87 – 94. · Zbl 0298.60015 · doi:10.1007/BF00533478 · doi.org
[9] H. Hering, Refined positivity theorem for semigroups generated by perturbed elliptic differential operators (to appear). · Zbl 0374.47020
[10] C. C. Heyde, Some almost sure convergence theorems for branching processes, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 20 (1971), 189 – 192. · Zbl 0212.19703 · doi:10.1007/BF00534900 · doi.org
[11] C. C. Heyde and J. R. Leslie, Improved classical limit analogues for Galton-Watson processes with or without immigration, Bull. Austral. Math. Soc. 5 (1971), 145 – 155. · Zbl 0219.60070 · doi:10.1017/S0004972700047018 · doi.org
[12] H. Kesten and B. P. Stigum, Additional limit theorems for indecomposable multidimensional Galton-Watson processes, Ann. Math. Statist. 37 (1966), 1463 – 1481. · Zbl 0203.17402 · doi:10.1214/aoms/1177699139 · doi.org
[13] J. R. Leslie, Some limit theorems for Markov branching processes, J. Appl. Probability 10 (1973), 299 – 306. · Zbl 0283.60088
[14] P. Levy, Theorie de l’addition des variables aleatoires, 2ième ed., Gauthier-Villars, Paris, 1954.
[15] Paul-André Meyer, Martingales and stochastic integrals. I. Lecture Notes in Mathematics. Vol. 284, Springer-Verlag, Berlin-New York, 1972. · Zbl 0239.60001
[16] Jacques Neveu, Mathematical foundations of the calculus of probability, Translated by Amiel Feinstein, Holden-Day, Inc., San Francisco, Calif.-London-Amsterdam, 1965. · Zbl 0137.11301
[17] William F. Stout, A martingale analogue of Kolmogorov’s law of the iterated logarithm, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 15 (1970), 279 – 290. · Zbl 0209.49004 · doi:10.1007/BF00533299 · doi.org
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