带重置的三维莫兰步

Symmetry Pub Date : 2024-09-18 DOI:10.3390/sym16091222
Mohamed Abdelkader
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引用次数: 0

摘要

在本文中,我们提出研究一个三维莫兰模型(Xn(1),Xn(2),Xn(3)),其中每个随机行走(Xn(i))∈{1,2,3}在每个时间单位增加一个单位或重置为零。我们通过矩生成工具分析其最终高度 Xn=max(Xn(1),Xn(2),Xn(3)) 的联合规律。此外,我们还证明了每种随机游走的极限分布都遵循参数为 1-qi 的移位几何分布,并分析了这三种游走的最大值,同时给出了均值和方差的明确表达式。
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Three-Dimensional Moran Walk with Resets
In this current paper, we propose to study a three-dimensional Moran model (Xn(1),Xn(2),Xn(3)), where each random walk (Xn(i))∈{1,2,3} increases by one unit or is reset to zero at each unit of time. We analyze the joint law of its final altitude Xn=max(Xn(1),Xn(2),Xn(3)) via the moment generating tools. Furthermore, we show that the limit distribution of each random walk follows a shifted geometric distribution with parameter 1−qi, and we analyze the maximum of these three walks, also giving explicit expressions for the mean and variance.
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