马春华. 带移民分枝过程的波动极限定理及其统计应用[J]. 应用概率统计, 2022, 38(3): 454-474. DOI: 10.3969/j.issn.1001-4268.2022.03.009
引用本文: 马春华. 带移民分枝过程的波动极限定理及其统计应用[J]. 应用概率统计, 2022, 38(3): 454-474. DOI: 10.3969/j.issn.1001-4268.2022.03.009
shu
MA Chunhua. A Fluctuation Limit Theorem of Branching Processes with Immigration and Statistical Applications[J]. Chinese Journal of Applied Probability and Statistics, 2022, 38(3): 454-474. DOI: 10.3969/j.issn.1001-4268.2022.03.009
Citation: MA Chunhua. A Fluctuation Limit Theorem of Branching Processes with Immigration and Statistical Applications[J]. Chinese Journal of Applied Probability and Statistics, 2022, 38(3): 454-474. DOI: 10.3969/j.issn.1001-4268.2022.03.009
shu

带移民分枝过程的波动极限定理及其统计应用

A Fluctuation Limit Theorem of Branching Processes with Immigration and Statistical Applications

    摘要
  • 摘要: 我们建立了带移民Galton-Watson分枝过程的波动极限定理, 其极限过程为由谱正勒维过程驱动的非时齐Ornstein-Uhlenbeck型过程.作为定理的统计应用,我们得到了后代分布的期望与移民分布的期望的条件最小二乘的渐近估计.

     

    Abstract: We prove a general fluctuation limit theorem for Galton-Watson branching processes with immigration. The limit is a time-inhomogeneous OU type process driven by a spectrally positive L\'evy process. As applications of this result, we obtain some asymptotic estimates for the conditional least squares estimators of the means of the offspring and immigration distributions.

     

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