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Critical Markov branching processes with general set of types. (English) Zbl 0232.60067

##### MSC:
 60J80 Branching processes (Galton-Watson, birth-and-death, etc.)
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##### References:
 [1] V. P. Čistjakov, Two limit theorems for branching processes with $$n$$ types of particles, Teor. Verojatnost. i Primenen. 4 (1959), 477-478 = Theor. Probability Appl. 4 (1959), 436-437. [2] Theodore E. Harris, The theory of branching processes, Die Grundlehren der Mathematischen Wissenschaften, Bd. 119, Springer-Verlag, Berlin; Prentice-Hall, Inc., Englewood Cliffs, N.J., 1963. · Zbl 1037.60001 [3] Einar Hille and Ralph S. Phillips, Functional analysis and semi-groups, American Mathematical Society Colloquium Publications, vol. 31, American Mathematical Society, Providence, R. I., 1957. rev. ed. · Zbl 0078.10004 [4] Nobuyuki Ikeda, Masao Nagasawa, and Shinzo Watanabe, Branching Markov processes. I, J. Math. Kyoto Univ. 8 (1968), 233 – 278. · Zbl 0233.60068 [5] A. Joffe and F. Spitzer, On multitype branching processes with \?\le 1, J. Math. Anal. Appl. 19 (1967), 409 – 430. · Zbl 0178.19504 · doi:10.1016/0022-247X(67)90001-7 · doi.org [6] Samuel Karlin, Positive operators, J. Math. Mech. 8 (1959), 907 – 937. · Zbl 0087.11002 [7] M. G. Kreĭn and M. A. Rutman, Linear operators leaving invariant a cone in a Banach space, Uspehi Matem. Nauk (N. S.) 3 (1948), no. 1(23), 3 – 95 (Russian). · Zbl 0030.12902 [8] J. E. Moyal, The general theory of stochastic population processes, Acta Math. 108 (1962), 1 – 31. · Zbl 0128.40302 · doi:10.1007/BF02545761 · doi.org [9] T. W. Mullikin, Limiting distributions for critical multitype branching processes with discrete time, Trans. Amer. Math. Soc. 106 (1963), 469 – 494. · Zbl 0114.08201 [10] Kôsaku Yosida and Shizuo Kakutani, Operator-theoretical treatment of Markoff’s process and mean ergodic theorem, Ann. of Math. (2) 42 (1941), 188 – 228. · JFM 67.0417.01 · doi:10.2307/1968993 · doi.org
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