Abstract
A limit theorem regarding the convergence of a sequence of normalized Bellman-Harris processes to an Jirina process (a branching process with a continuous phase space) is obtained.
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Literature cited
S. A. Aliev, “A limit theorem for Bellman-Harris processes,” in: Some Questions on the Theory of Random Processes [in Russian], Akad. Nauk UkrSSR, Int. Mat., Kiev (1984), pp. 3–10.
V. M. Shurenkov, “Transition phenomena of renewal theory in asymptotic problems in the theory of random processes. I,” Mat. Sb.,112 (154), No. 1, 115–132 (1980).
S. A. Aliev and V. M. Shurenkov, “Transition phenomena and the convergence of Galton-Watson processes to Jirina processes,” Teor. Veroyatn. Primen.,27, No. 3, 443–455 (1982).
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 6, pp. 827–832, June, 1990.
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Aliev, S.A. Convergence of Bellman-Harris branching processes. Ukr Math J 42, 730–734 (1990). https://doi.org/10.1007/BF01058923
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DOI: https://doi.org/10.1007/BF01058923