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Critical Bellman-Harris branching processes starting with a large number of particles. (English. Russian original) Zbl 0659.60117
Math. Notes 40, 803-811 (1986); translation from Mat. Zametki 40, No. 4, 527-541 (1986).
See the review in Zbl 0621.60092.

MSC:
60J80 Branching processes (Galton-Watson, birth-and-death, etc.)
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References:
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[2] T. E. Harris, The Theory of Branching Processes, Springer, Berlin (1963). · Zbl 0117.13002
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[9] A. L. Yakymiv, ?The asymptotic behavior of the probabilities of the extensions of critical Bellman-Harris processes,? Tr. Mat. Inst. Akad. Nauk SSSR,177, 177-205 (1986). · Zbl 0607.60075
[10] B. V. Gnedenko and A. N. Kolmogorov, Limit Distributions for Sums of Independent Random Variables, Addison-Wesley, Reading (1954). · Zbl 0056.36001
[11] R. S. Slack, ?A branching process with mean one and possibly infinite variance,? Z. Wahrsch. Verw. Gebiete,9, No. 2, 139-145 (1968). · Zbl 0164.47002 · doi:10.1007/BF01851004
[12] W. Feller, An Introduction to Probability Theory and Its Applications, Vol. II, Wiley, New York (1966). · Zbl 0138.10207
[13] E. Seneta, Regularly Varying Functions, Lecture Notes in Math., No. 508, Springer, Berlin (1976). · Zbl 0324.26002
[14] S. G. Tkachuk, ?Theorems on large deviations in the case of distributions with regularly varying tails,? in: Random Processes and Statistical Inference, No. 5 [in Russian], Fan, Tashkent (1975), pp. 164-174.
[15] A. N. Kolmogorov and S. Fomin, Elements of the Theory of Functions and Functional Analysis [in Russian], Nauka, Moscow (1972). · Zbl 0235.46001
[16] V. A. Vatutin and S. M. Sagitov, ?Decomposable branching processes with two types of particles,? Trudy Mat. Inst. Akad. Nauk SSSR,177, 3-20 (1986). · Zbl 0619.60079
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