对于离散时间下临界 CMJ 过程, 考虑未来代 (the cominggeneration) 的个体数目. 利用更新定理, 在家族树不灭亡的条件下,得到条件过程的极限定理.从而能够从未来代的信息来分析离散时间下临界分支过程的极限性质.
Abstract
We consider the count of the coming generation of subcritical CMJ processes in discrete time. With the help of several renewal theorems, we obtain the limit theorems for the conditional processes. Therefore, we show how the coming generation sheds new light on the limit properties of subcritical CMJ processes.
关键词
离散时间 /
下临界 /
更新方程 /
未来代
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Key words
discrete time /
subcritical /
renewal theory /
the coming generation
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参考文献
[1] Athreya K. B., Ney P. E., Branching Processes, Springer-Verlag, Berlin, 1972.
[2] Feller W., An Introduction to Probability Theory and Its Applications II, John Wiley & Sons, New York, 1966.
[3] Heathcote C. R., Seneta E., Vere-Jones D., A refinement of two theorems in the theory of branching processes, Theor. Probab. Appl., 1967, 12: 297-301.
[4] Jagers P., Branching Processes with Biological Applications, John Wiley & Sons, Ltd, 1975.
[5] Jagers P., Nerman O., The growth and composition of branching populations, Adv. in Appl. Probab., 1984: 221-259.
[6] Jagers P., Sagitov S., General branching processes in discrete time as random trees, Bernoulli, 2008, 14(4): 949-962.
[7] Kolmogorov A., On the solution of a problem in biology, Izv. NII Mat. Mekh. Tomsk. Univ., 1938, 2: 7-12.
[8] Lyons R., Pemantle R., Peres Y., Conceptual proofs of l log l criteria for mean behavior of branching processes, Ann. Probab., 1995, 23(3): 1125-1138.
[9] Nerman O., On the convergence of supercritical general (CMJ) branching processes, Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete, 1981, 57(3): 365-395.
[10] Olofsson P., The xlogx condition for general branching processes, J. Appl. Probab., 1998, 35(3): 537-544.
[11] Yaglom A. M., Certain limit theorems of the theory of braching processes, Dokl. Acad. Nauk SSSR, 1947, 56: 795-798.
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