论文标题
分析一些完全可解决的urn模型
Analysis of some exactly solvable diminishing urn models
论文作者
论文摘要
我们研究了具有\ emph {nighining}字符的几种准确可解决的polya-eggenberger urn模型，即指定颜色的球，例如$ x $在有限数量的绘图后完全绘制。这里的主要兴趣是当颜色$ x $完全删除时留下的球数。我们考虑了先前在文献中研究的几种减少的尿液，例如药丸问题，食人族urn和确定的畜栏问题，并得出了精确而有限的分布。我们的方法基于通过生成函数和部分微分方程来解决复发。
We study several exactly solvable Polya-Eggenberger urn models with a \emph{diminishing} character, namely, balls of a specified color, say $x$ are completely drawn after a finite number of draws. The main quantity of interest here is the number of balls left when balls of color $x$ are completely removed. We consider several diminishing urns studied previously in the literature such as the pills problem, the cannibal urns and the OK Corral problem, and derive exact and limiting distributions. Our approach is based on solving recurrences via generating functions and partial differential equations.
