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A limit theorem for population-size-dependent branching processes
Published online by Cambridge University Press: 14 July 2016
Abstract
An analogue of the Kesten–Stigum theorem, and sufficient conditions for the geometric rate of growth in the rth mean and almost surely, are obtained for population-size-dependent branching processes.
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References
[1]
Cohn, H. (1977) On the norming constants occurring in convergent Markov chains. Bull. Austral. Math. Soc.
17, 193–205.Google Scholar
[2]
Cohn, H. (1982) On the fluctuation of stochastically monotone Markov chains and some applications. J. Appl. Prob.
20, 178–184.Google Scholar
[3]
Fujimagari, T. (1976) Controlled Galton–Watson process and its asymptotic behaviour. Kodai Math. Sem. Rep.
27, 11–18.Google Scholar
[4]
Höpfner, R. (1985) On some classes of population-size-dependent Galton–Watson processes. J. Appl. Prob.
22, 25–36.Google Scholar
[5]
Jagers, P. (1975) Branching Processes with Biological Applications.
Wiley, New York.Google Scholar
[6]
Klass, M. (1976) Toward a universal law of the iterated logarithm. Z. Wahrslichkeitsth.
36, 165–178.Google Scholar
[7]
Klebaner, F. C. (1983) Population-size-dependent branching process with linear rate of growth. J. Appl. Prob.
20, 242–250.Google Scholar
[8]
Klebaner, F. C. (1983) Population-size-dependent Branching Processes. , University of Melbourne.Google Scholar
[9]
Klebaner, F. C. (1984) On population-size-dependent branching processes. Adv. Appl. Prob.
16, 30–55.Google Scholar
[10]
Klebaner, F. C. (1984) Geometric rate of growth in population-size-dependent branching processes. J. Appl. Prob.
21, 40–49.Google Scholar
[11]
Labrovskii, V. A. (1972) A limit theorem for generalized branching process depending on the size of the population. Theory Prob. Appl.
17, 72–85.CrossRefGoogle Scholar
[12]
Levina, L. V., Leontovich, A. M. and Pyatetskii-Shapiro, I. I. (1968) On regulative branching process. Problemy peredachi informatsii
4, 72–82.Google Scholar
[13]
Lipow, C. (1977) Limiting diffusions for population-size-dependent branching processes. J. Appl. Prob.
14, 14–24.Google Scholar
[15]
Von Bahr, B. and Esseen, C. G. (1965) Inequalities for the rth absolute moment of a sum of random variables, 1 ≦ r ≦ 2. Ann. Math. Statist.
36, 299–303.Google Scholar
[16]
Zubkov, A. M. (1974) Analogies between Galton–Watson processes and ?-branching processes. Theory Prob. Appl.
19, 309–331.Google Scholar
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