有限矩条件下变化环境中分枝过程的收敛定理

Acta mathematica scientia,Series A ›› 2016, Vol. 36 ›› Issue (2): 353-361.

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Convergence of Branching Process in Varying Environments when All Moments Being Finite

Wang Weigang¹, Yang Guangyu², Gao Zhenlong³

1 School of Statistics and Mathematics, Zhejiang Gongshang University, Hangzhou 310018;
2 School of mathematics, Zhengzhou university, Zhengzhou 450001;
3 School of mathematics, Qufu normal university, Shandong Qufu 273165

Received:2015-08-01 Revised:2016-01-08 Online:2016-04-25 Published:2016-04-25
Supported by:
Supported by the Natural Science Foundation of Zhejiang Province (LY13A010003), the NSFC (11371321, 11201420), Humanities and Social Sciences Foundation of Ministry of Education (10YJC790091), Foundation of Zhejiang Educational Committee (Y201326953)

Abstract

Abstract:

In this paper, we studied convergence theorems of the branching processes in varying environments. When the environment is not independence, at the moment conditions of the environment, we prove that W_nW and W>0, a.s. firstly, and then we give the central limit theorem of the process, at last we give the law of the iterated logarithm of log Z_n. Those results are very important to the other asymptotic properties and deviations of the process.

Key words: Branching process, Random environments, Central limit theorem, LIL

CLC Number:

O211.62

Wang Weigang, Yang Guangyu, Gao Zhenlong. Convergence of Branching Process in Varying Environments when All Moments Being Finite[J].Acta mathematica scientia,Series A, 2016, 36(2): 353-361.

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Convergence of Branching Process in Varying Environments when All Moments Being Finite

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