| 随机环境中受控分枝过程的极限定理 |
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| 引用本文： | 李应求,李德如,潘生,彭雪莲.随机环境中受控分枝过程的极限定理[J].数学学报,2018,61(2):317-326. |
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| 作者姓名： | 李应求 李德如 潘生 彭雪莲 |
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| 作者单位： | 1. 长沙理工大学数学与统计学院 长沙 410114;
2. 长沙理工大学土木与建筑学院 长沙 410114;
3. 上海财经大学统计与管理学院 上海 200433 |
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| 基金项目： | 国家自然科学基金资助项目（11571052）；湖南省自然科学基金（2017JJ2271，2017JJ2274）；长沙理工大学研究生科研创新项目（CX2017SS24） |
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| 摘 要： | 讨论了随机环境中受控分枝过程{Z_n:n∈N}的极限问题.给出了过程在{S_n:n∈N}下的规范化过程{W_n:n∈N}几乎处处收敛、L~1收敛和L~2收敛的充分条件,以及过程{W:n∈N}的极限非退化于0的充分条件和必要条件,得到了过程在{I_n:n∈N}下的规范化过程{W_n:n∈N}几乎处处收敛和L~1收敛的充分条件.
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| 关 键 词： | 随机环境 受控分枝过程 规范化 几乎处处收敛 L~1收敛 |
Limit Theorems for Controlled Branching Processes in Random Environments |
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| Ying Qiu LI,De Ru LI,Sheng PAN,Xue Lian PENG.Limit Theorems for Controlled Branching Processes in Random Environments[J].Acta Mathematica Sinica,2018,61(2):317-326. |
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| Authors: | Ying Qiu LI De Ru LI Sheng PAN Xue Lian PENG |
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| Institution: | 1. School of Mathematics and Statistics, Changsha University of Science and Technology, Changsha 410114, P. R. China;
2. School of Civil Engineering and Architecture, Changsha University of Science and Technology, Changsha 410114, P. R. China;
3. School of Statistics and Management, Shanghai University of Finance and Economics, Shanghai 200433, P. R. China |
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| Abstract: | The limiting behaviors for controlled branching processes in random environments are discussed. Under the normalization factor {Sn:n ∈ N}, the normalization processes {?n:n ∈ N} of are studied, and the sufficient conditions of {?n:n ∈ N} a.s., L1 and L2 convergence are given; A sufficient condition and a necessary condition for convergence to a non-degenerate at 0 random variable are got; Under the normalization factor {In:n ∈ N}, the normalization processes {Wn:n ∈ N} are discussed, and the sufficient conditions of {Wn:n ∈ N} a.s., and L1 convergence are obtained. |
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| Keywords: | random environment controlled branching processes normalize almost everywhere convergent L1 convergent |
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