带有移民的上临界Markov分支过程的下偏差概率
Lower Deviation Probabilities for Supercritical Markov Branching Processes with Immigration
DOI: 10.12677/pm.2024.144122, PDF,   
作者: 彭 超*, 王 娟：上海理工大学理学院，上海
关键词: 下偏差；上临界；分支过程；移民；Lower Deviation； Supercritical； Branching Process； Immigration
摘要: 设{Z(t);t≥0}为具有迁移的连续时间上临界分支过程(MBPI)，其子代均值为m(t)。本文主要研究当t→∞时，的下偏差概率，具体包括局部下偏差概率P(Z(t)=kt)和总体下偏差概率P(0≤Z(t)≤kt。此外，我们还给出了局部极限定理和一些相关的估计。对于我们的证明，我们使用了著名Cramer方法来证明自变量和的大偏差，以满足我们的需要。
Abstract: Let {Z(t);t≥0} be a continuous-time supercritical branching process with immigration (MBPI) with offspring mean m(t). In this paper, we mainly research the local lower deviation probabilities P(Z(t)=kt) and overall lower deviation probabilities P(0≤Z(t)≤kt with  as t→∞. Moreover, we present the local limit theorem and some related estimates of this MBPIs. For our proofs, we use the well-known Cramer method to prove the large deviation of the sum of independent variables to satisfy our needs.
文章引用：彭超, 王娟. 带有移民的上临界Markov分支过程的下偏差概率[J]. 理论数学, 2024, 14(4): 164-169. https://doi.org/10.12677/pm.2024.144122

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