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随机环境中两性分枝过程的矩收敛准则

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随机环境中两性分枝过程的矩收敛准则 李应求, 肖胜, 彭朝晖长沙理工大学数学与统计学院, 长沙 410004 Moment Convergence Criteria for Bisexual Branching Processes in Random Environments LI Yingqiu, XIAO Sheng, PENG ZhaohuiSchool of Mathematics and Statistics, Changsha University of Science and Technology, Changsha 410004, China
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摘要设(Zn)是随机环境ξ中两性分枝过程,Ŵn=Zn/Sn,???20200402???=Zn/In,其中(Sn)和(In)是通常的规范化序列.给出了过程(ŴnLα-收敛(α≥1)到有限且非退化随机变量的充分条件和必要条件;通过鞅分解定理给出了(ŴnL2-收敛的充分条件;研究了过程(???20200402???)Lα-收敛(α≥1)到有限且非退化随机变量的充分条件,并给出了过程(???20200402???)L2-收敛的必要条件.
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收稿日期: 2019-04-25
PACS:O211.65
基金资助:国家自然科学基金(11571052,11731012),湖南省自然科学基金(2018JJ2417)以及湖南省研究生科研创新项目(CX2018B572)资助项目.

引用本文:
李应求, 肖胜, 彭朝晖. 随机环境中两性分枝过程的矩收敛准则[J]. 应用数学学报, 2020, 43(4): 639-653. LI Yingqiu, XIAO Sheng, PENG Zhaohui. Moment Convergence Criteria for Bisexual Branching Processes in Random Environments. Acta Mathematicae Applicatae Sinica, 2020, 43(4): 639-653.
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