变化环境下Galton-Watson过程的极限理论

王伟刚, 明瑞星, 甘建军

数学学报 ›› 2014, Vol. 57 ›› Issue (5) : 923-930.

PDF(368 KB)
中国科学院数学与系统科学研究院期刊网
PDF(368 KB)
数学学报 ›› 2014, Vol. 57 ›› Issue (5) : 923-930. DOI: 10.12386/A2014sxxb0085
论文

变化环境下Galton-Watson过程的极限理论

    王伟刚1, 明瑞星1, 甘建军2
作者信息 +

The Limit Theory of Galton-Watson Branching Process in Random Environment

    Wei Gang WANG1, Rui Xing MING1, Jian Jun GAN2
Author information +
文章历史 +

摘要

研究了变化环境下的Galton-Watson过程.当环境的期望和方差有限时，给出了几乎处处环境下的首达时极限定理，以及log Zn的大偏差定理.

Abstract

We studied the Galton-Watson process in varying environment. We gave the first hitting time of the process and the large deviation of log Zn at the almost sure environments when the mathematical expectation and variance of the environments are finite.

关键词

Galton-Watson过程 / 首达时 / 大偏差

Key words

Galton-Watson branching / the first hitting time / large deviation

引用本文

EndNote

Ris (Procite)

Bibtex

导出引用
王伟刚, 明瑞星, 甘建军. 变化环境下Galton-Watson过程的极限理论. 数学学报, 2014, 57(5): 923-930 https://doi.org/10.12386/A2014sxxb0085
Wei Gang WANG, Rui Xing MING, Jian Jun GAN. The Limit Theory of Galton-Watson Branching Process in Random Environment. Acta Mathematica Sinica, Chinese Series, 2014, 57(5): 923-930 https://doi.org/10.12386/A2014sxxb0085

参考文献

[1] Christian B., Götz K., Upper large deviations of branching processes in a random environment - Offspringdistributions with geometrically bounded tails, Stochastic Proc. Appl., 2010, 120(10): 2064-2077.

[2] Dembo A., Zeitouni O., Large Deviation Techniques and Applications, Springer, New York, 1998.

[3] Gao Z. L., Hu X. Y., Limit theorems for a Galton-Watson process in the i.i.d random environment, ActaMath. Sci., 2012, 32B(3): 1193-1205.

[4] Huang C. M., Liu Q. S., Moments, moderate and large deviations for a branching process in random environment,Stochastic Proc. Appl., 2012, 122: 522-545.

[5] Tanny D., Limit theorems for branching in a random environment, Ann. Prob., 1977, 5(1): 100-116.

[6] Vincent B., Christian B., Upper large deviations for branching processes in random environment with heavytails, Electron. J. Probab., 2011, 16(69): 1900-1933.

[7] Wang W. G., Bounds of deviation for branching chains in random environments, Acta Math. Sin., Engl.Series, 2011, 27(5): 897-904.

[8] Wang W. G., Lv P., Hu D. H., Harmonic moments of branching processes in random environments, ActaMath. Sin., Engl. Series, 2009, 25(7): 1087-1096.

基金

国家自然科学基金（11371321，11201420）；浙江省自然科学基金（LY13A010003，LQ12A01016）及浙江省教育厅课题（Y201326953）；浙江工商大学人文社科统计学基地资助项目

PDF(368 KB)

255

Accesses

0

Citation

Detail
段落导航
相关文章

/

〈 〉