| 随机环境中迁入分枝过程的极限性质 |
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| 引用本文： | 孙卫,刘伟,李德如.随机环境中迁入分枝过程的极限性质[J].数学理论与应用,2013(4):1-5. |
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| 作者姓名： | 孙卫 刘伟 李德如 |
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| 作者单位： | [1]长沙理工大学数学与计算科学学院,长沙410114 [2]湖南大学工商管理学院,长沙410082 |
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| 基金项目： | 本文获国家自然科学基金项目（11171044）;湖南省自然科学基金资助项目（11JJ2001）和高等学校博士学科点专项科研基金项目（20104306110001）资助 |
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| 摘 要： | 在方差和均值有限的条件下，得到了随机环境中迁入分枝过程对应的规范化过程的几乎处处收敛性和L^2收敛性．这对于刻画过程本身的发散速度，具有重要的意义．
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| 关 键 词： | 随机环境 迁入分枝过程 下鞅 几乎处处收敛 L^2收敛 |
Limit Properties for Branching Process with Immigration in Random Environment |
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| Sun Wei^,Liu Wei^,Li Deru.Limit Properties for Branching Process with Immigration in Random Environment[J].Mathematical Theory and Applications,2013(4):1-5. |
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| Authors: | Sun Wei^ Liu Wei^ Li Deru |
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| Institution: | 1(1. School of Mathematics and Computing Sciences, Changsha University of Science and Technology, Changsha 410114, China) (2. School of Business, Hunan University, Changsha 410082, China) |
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| Abstract: | In this paper, we study the almost everywhere convergence and L^2 convergence for a normalized branching process with immigration in random environments, assuming that the process has finite mean and variance. The con vergences play important roles in describing the rate of divergence for branching process with immigration in random environments. |
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| Keywords: | Random environment Branching process with immigration Submartingale Almost everywhere convergence L^2 convergence |
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