广义生灭分支过程存活后代数的分布

颜云志, 傅云斌, 王汉兴

数学学报 ›› 2014, Vol. 57 ›› Issue (3) : 593-600.

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数学学报 ›› 2014, Vol. 57 ›› Issue (3) : 593-600. DOI: 10.12386/A2014sxxb0055
论文

广义生灭分支过程存活后代数的分布

    颜云志1,3, 傅云斌1,2, 王汉兴1
作者信息 +

The Surviving Descendent Distributions in General Birth-Death Branching Processes

    Yun Zhi YAN1,3, Yun Bin FU1,2, Han Xing WANG1
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文章历史 +

摘要

考虑一个生物种群生灭分支过程,其中个体繁衍后代的出生率与死亡率均为依赖时间的函数. 在通常的（条件）独立性假设条件下, 用生成函数方法给出了任意个体在给定时刻仍存活或已死亡条件下其存活后代数的分布, 进而给出了个体在已知其“生卒时刻”, 任意时刻存活后代数的分布.

Abstract

We investigate a model of birth-death branching processes, of which some (conditional) independence is assumed and the birth and death rates for each surviving individual are both time dependent. Given a time that an individual is alive (or is dead), the conditional distribution of its surviving descendant number is obtained. Furthermore, assume that an individual's birth and death times are both given, the distribution of its surviving descendant number at any given time is deduced.

关键词

生灭分支过程模型 / 概率生成函数 / 一阶线性偏微分方程 / 存活后代数

Key words

model for birth-death branching process / probability generating function / first order liner partial differential equation / surviving descendant number

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颜云志, 傅云斌, 王汉兴. 广义生灭分支过程存活后代数的分布. 数学学报, 2014, 57(3): 593-600 https://doi.org/10.12386/A2014sxxb0055
Yun Zhi YAN, Yun Bin FU, Han Xing WANG. The Surviving Descendent Distributions in General Birth-Death Branching Processes. Acta Mathematica Sinica, Chinese Series, 2014, 57(3): 593-600 https://doi.org/10.12386/A2014sxxb0055

参考文献

[1] Athreya K. B., Karlin S., On branching processes with random environments (I), (II), Annals of Math. Stat., 1971, 42: 1499-1520; 1843-1858.
[2] Athreya K. B., Ney P. E., Branching Processes, Springer-Verlag, Berlin, 1972.
[3] Bellman R., Harris T., On age-dependent binary branching processes, Annals of Mathematics, 1952, 55: 280-295.
[4] Feller W., Die grundlagen der volterraschen theorie des kampfes ums dasein in wahrscheinlichkeitstheoretischer behandlung, Acta Biotheoretica, 1939, 5(1): 11-40.
[5] Harris T. E., The Theory of Branching Processes, Springer-Verlag, Berlin, 1963.
[6] Hu Y. L., Wu Q. P., Li Y. Q., Explosiveness of age-dependent branching processes in random environments, Acta Mathematica Sinica, Chinese Series, 2010, 53(5): 1027-1034.
[7] Kendall D G, On the generalized “birth-and-death” process, Annals of Math. Stat., 1948, 19(1): 1-15.
[8] Li Y. Q., Li X., Liu Q. S., A random walk with a branching system in random environments (in Chinese), Sci. China, Ser. A, 2007, 37(3): 341-347.
[9] Li Y. Q., Liu Q. S., Age-dependent branching processes in random environments (in Chinese), Sci. China, Ser. A, 2008, 38(7): 799-818.
[10] Smith W. L., Wilkinson W. E., On branching processes in random environments, Annals of Math. Stat., 1969, 40: 814-827.
[11] Wang H. X., Extinction of P-S-D branching processes in random environments, J. Appl. Probab., 1999, 36(1): 146-154.
[12] Wang H. X., Multitype branching close walks in random environments (in Chinese), Chinese Sci. Bull., 1995, 40(7): 586-589.
[13] Wang H. X., Dai Y. L., Population-size-dependent branching processes in markovian random environments, Chinese Sci. Bull., 1998, 43(8): 635-638.
[14] Wang H. X., Fang D. F., Asymptotic behaviour for P-S-D branching processes in markovian random environments, J. Appl. Probab., 1999, 36(2): 611-619.
[15] Wang H. X., Zhao F., Lu J. Y., A note on asymptotic behavior of Galton-Watson branching processes in random environments, J. Shanghai Univ. (English Edition), 2006, 10(2): 95-99.

基金

国家自然科学基金（60872060/11101284）；Levelhulme Trust Visiting Fellowships（2011-2012）；上海市自然科学基金（12ZR1421000）及上海市教委创新项目（12ZZ193/14yz152）；上海市市本级财政部门预算项目（1138IA0005）
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