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References
Asmussen, S.: Some martingale methods in the limit theory of supercritical branching processes. In Advances in Probability and Related Topics (ed. P. Ney). New York: Marcel Dekker 1978
Asmussen, S., Kaplan, N.: Branching random walks II. Stochastic Processes Appl. 4, 15–31 (1976)
Bahadur, R.R., Ranga Rao, R.: On deviation of the sample mean. Ann. Math. Statist. 31, 1015–1027 (1960)
Biggins, J.D.: Martingale convergences in the branching random walk. J. Appl. Probability 14, 25–37 (1977)
Biggins, J.D.: Chernoffs theorem in the branching random walk. J. Appl. Probability 14, 630–636 (1977)
Bingham, N.H., Doney, R.A.: Asymptotic properties of supercritical branching processes. I: the Galton-Watson process. Advances in Appl. Probability 6, 711–731 (1974)
Bingham, N.H., Doney, R. A.: Asymptotic properties of supercritical branching processes. II: Crump-Mode and Jirina processes. Advances in Appl. Probability 7, 66–82 (1975)
Breiman, L.: Probability. London: Addison-Wesley 1968
Feller, W.: An Introduction to Probability Theory and its Applications. Volume II. New York: Wiley 1971
Gnedenko, B.V., Kolmogorov, A.N.: Limit distributions for sums of independent random variables London: Addison-Wesley 1954
Kesten, H., Stigum, B. P.: Limit theorems for decomposable multi-dimensional Galton-Watson processes. J. Math. Anal. Appl. 17, 309–338 (1967)
Kingman, J.F.C.: The first birth problem for an age-dependent branching process. Ann. Probability 3, 790–801 (1975)
Kurtz, T.G.: Inequalities for the law of large numbers. Ann. Math. Statist. 43, 1874–1883 (1972)
Matthes, K., Kerstan, J., Mecke, J.: Infinitely divisible point processes. Translated from the German edition. New York: Wiley 1978
Stone, C.J.: A local limit theorem for multidimensional distribution functions. Ann. Math. Statist. 36, 546–551 (1965)
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Biggins, J.D. Growth rates in the branching random walk. Z. Wahrscheinlichkeitstheorie verw Gebiete 48, 17–34 (1979). https://doi.org/10.1007/BF00534879
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DOI: https://doi.org/10.1007/BF00534879