上临界Markov分支过程的调和矩
Harmonic Moment of the Supercritical Markov Branching Process
摘要: 设{Z(t);t≥0}是一个上临界马尔可夫分支过程。本文研究了带移民上临界分支过程在连续时间情况下调和矩E[Z(t)]−r的收敛速度，它在大偏差及中心极限定理的研究中具有重要作用。推广了已有文献中无移民情况的相应结果，经研究发现该收敛存在相变，这一相变由b1+a0+mr与0的大小关系所决定。这里使用的方法与离散的情况有所不同，我们提出了一种新的区间划分的方法来得出结论。同时作为副产品我们得到了连续时间下带移民分支过程的一个泛函方程。
Abstract: Support {Z(t);t≥0} be a supercritical Markov branching processes. In this paper, we study the convergence rate of harmonic moments E[Z(t)]−r of the Supercritical Markov branching process with immigration in continuous time, it plays an important role in the study of the large deviation and the central limit theorem. The corresponding results in the existing literature are generalized. It is found that there is a variant of the convergence, and the variant b1+a0+mr is related to the size of 0. Different from the discrete case, we propose a new interval division method to reach the conclusion. As a by-product we obtain a functional equation with migration branching process in continuous time.
文章引用：肖宁洁, 王娟. 上临界Markov分支过程的调和矩[J]. 理论数学, 2023, 13(4): 846-853. https://doi.org/10.12677/PM.2023.134089

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