Markov分支过程的调和矩
Harmonic Moments for the Supercritical Markov Branching Processes
DOI: 10.12677/PM.2022.121016, PDF,    国家自然科学基金支持
作者: 王雪珂, 王 娟*：上海理工大学理学院，上海
关键词: Markov分支过程；上临界；调和矩；大偏差；Markov Branching Process； Supercritical； Harmonic Moment； Large Deviation
摘要: 假设{Z(t);t≥0}是上临界的Markov分支过程，本文主要研究了该过程调和矩的收敛速率，研究发现，该收敛速度存在相变，并且该相变取决于mr+b1 > 0，mr+b1=0或mr+b1 < 0；作为应用，本文还进一步讨论了Z(t+s)/Z(t)的大偏差速率。
Abstract: Suppose that {Z(t);t≥0} be a supercritical Markov branching process. The paper mainly studies the convergence rate of the harmonic moment of the process. We find that there is a phase transition for convergence rates, which depends on mr+b1 > 0, =0 or < 0. As an application, the large deviation rate Z(t+s)/Z(t) is discussed in this paper.
文章引用：王雪珂, 王娟. Markov分支过程的调和矩[J]. 理论数学, 2022, 12(1): 117-124. https://doi.org/10.12677/PM.2022.121016

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