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On the convergence of supercritical general (C-M-J) branching processes. (English) Zbl 0451.60078

MSC:
60J80Branching processes
60G55Point processes
References:
[1]Asmussen, S., Kurtz, T.G.: Necessary and sufficient conditions for complete convergence in the law of large numbers. Ann. Probability 8, 176-182 (1980) · Zbl 0426.60026 · doi:10.1214/aop/1176994835
[2]Athreya, K.B.: On the supercritical agedependent branching process. Ann. Math. Statist. 40, 743-763 (1969) · Zbl 0175.46603 · doi:10.1214/aoms/1177697585
[3]Athreya, K.B., Kaplan, N.: Convergence of the age distribution in the one-dimensional supercritical age-dependent branching process. Ann. Probability 4, 38-50 (1976) · Zbl 0356.60048 · doi:10.1214/aop/1176996179
[4]Athreya, K.B., Kaplan, N.: The additive property and its applications in branching processes. Adv. in Probability vol 5, branching processes (1978)
[5]Bauer, H.: Wahrscheinlichkeitstheorie und Grundzüge der Massteorie. Berlin: de Gruyter, 1968
[6]Breiman, L.: Probability. Reading, Massachusetts: Addison Wesley, 1968
[7]Doney, R.A.: A limit theorem for a class of supercritical branching processes. J. Appl. Probability 9, 707-724 (1972) · Zbl 0267.60082 · doi:10.2307/3212610
[8]Doney, R.A.: On single- and multi-type general age-dependent branching processes. J. Appl. Probability 13, 239-246 (1976) · Zbl 0365.60080 · doi:10.2307/3212827
[9]Härnqvist, M.: Limit theorems for point processes generated in a general branching process. To appear in Adv. Appl. Prob. (1981)
[10]Jagers, P.: Branching Processes with Biological Applications. London: Wiley, 1975
[11]Jagers, P.: How probable is it to be first-born? And other branching process applications to kinship problems. To appear in Mathematical Biosciences (1981)
[12]Kesten, H., Stigum, B.P.: A limit theorem for multidimensional Galton-Watson processes. Ann. Math. Statist. 37, 1211-1223 (1966) · Zbl 0203.17401 · doi:10.1214/aoms/1177699266
[13]Kuczek, T.: On the convergence of the empiric age distribution for one dimensional super-critical age dependent branching processes. Rutgers University, New Brunswick, New Jersey (1980). To appear in Ann. Probability
[14]Meyer, P.-A.: Martingales and Stochastic Integrals I. Berlin Heidelberg New York: Springer, 1972
[15]Nerman, O.: On the Convergence of Supercritical General Branching Processes. Thesis, Department of Mathematics, Chalmers University of Technology and the University of Göteborg 1979
[16]Neveu, J.: Discrete-Parameter Martingales. Amsterdam: North-Holland, 1975
[17]Rama-Murthy, K.: Convergence of State Distributions in Multitype Bellman-Harris and Crump-Mode-Jagers Branching Processes. Thesis, Department of Appl. Math. Bangalore: Indian Institute of Science, 1978
[18]Savits, T.H.: The Supercritical Multi-Type Crump and Mode Age-dependent Model. Unpublished manuscript, University of Pittsburgh, 1975