随机环境中依赖年龄分枝过程的爆炸问题

胡杨利, 吴庆平, 李应求

数学学报 ›› 2010, Vol. 53 ›› Issue (5) : 1027-1034.

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数学学报 ›› 2010, Vol. 53 ›› Issue (5) : 1027-1034. DOI: 10.12386/A2010sxxb0114
论文

随机环境中依赖年龄分枝过程的爆炸问题

    胡杨利1, 吴庆平2, 李应求1
作者信息 +

Explosiveness of Age-Dependent Branching Processes in Random Environments

    Yang Li HU1, Qing Ping WU2, Ying Qiu LI1
Author information +
文章历史 +

摘要

讨论了随机环境中依赖年龄分枝过程中的爆炸问题,得到了过程爆炸的判定定理以及关于两个过程爆炸的比较定理.

 

Abstract

The problem of explosiveness of age-dependent branching processes in random environments is discussed, then some sufficient and necessary conditions and more sufficient conditions of explosiveness are obtained. It is seen that explosiveness is essentially determined by the steepness of random life-length distribution function near the origin and random family-size generating function near 1. Also it's shown ways to compare two different processes.

 

关键词

随机环境 / 依赖年龄分枝过程 / 爆炸问题

Key words

random environment / age-dependent branching process / explosiveness

引用本文

导出引用
胡杨利, 吴庆平, 李应求. 随机环境中依赖年龄分枝过程的爆炸问题. 数学学报, 2010, 53(5): 1027-1034 https://doi.org/10.12386/A2010sxxb0114
Yang Li HU, Qing Ping WU, Ying Qiu LI. Explosiveness of Age-Dependent Branching Processes in Random Environments. Acta Mathematica Sinica, Chinese Series, 2010, 53(5): 1027-1034 https://doi.org/10.12386/A2010sxxb0114

参考文献


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[9] Hu Y. L., Yang X. Q., Li Y. Q., Theorem of equivalence about the branching processes in random environments, Acta Math. Appl., 2007, 30(3): 411--421 (in Chinese).

[10] Li Y. Q., Hu Y. L., Calculating extinction probabilities for generalized random walks in random environments, Acta Math. Scie., 2006, 26(3): 476--480 (in Chinese).

[11] Li Y. Q., Recurrent markov chains in Bi-infinite random environments, Acta Mathematica Sinica, Chinese Series, 2007, 50(5): 1099--1110.

[12] Li Y. Q., Wang S. M., Hu Y. L., Relationships among markov chains in random environments and joint markov chains, Acta Mathematica Sinica, Chinese Series, 2006, 49(6): 1373--1380.

[13] Li Y. Q., Li X., Liu Q. S., A random walk with a branching system in random environments, Science in China A, 2007, 50(5): 698--704.

[14] Li Y. Q., Transience of markov chains in Bi-infinite random environments, Acta Math. Scie., 2007, 27(2): 269--276 (in Chinese).

基金

国家自然科学基金项目(10471012;10771021);教育部留学回国人员科研启动基金项目([2005]564)

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