一类精确可解的递减瓮模型的分析
Analysis of some exactly solvable diminishing urn models
摘要：
本文研究了几个具有\emph{diminishing}特征的精确可解的Polya-Eggenberger瓮模型，即特定颜色的球，比如说$x$在有限次绘制后被完全绘制.这里主要关注的数量是当颜色为$x$的球被完全移除时剩下的球的数量。我们考虑几个递减瓮研究以前在文献中，如药丸问题，食人瓮和OK畜栏问题，并获得精确的和限制的分布。我们的方法是基于解决递归通过生成函数和偏微分方程。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
