We study the infinite urn scheme when the balls are sequentially distributed over an infinite number of urns labeled 1,2,... so that the urn j at every draw gets a ball with probability \(p_j\), where \(\sum _j p_j=1\). We prove functional central limit theorems for discrete time and the Poissonized version for the urn occupancies process, for the odd occupancy and for the missing mass processes extending the known non-functional central limit theorems.

中文翻译：

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无限瓮模型中占用和缺失质量过程的功能中心极限定理

当球顺序分布在标记为1,2，... _j p_j=1\)。我们证明了离散时间的函数中心极限定理和瓮占用过程的泊松版本，奇数占用和丢失质量过程扩展了已知的非函数中心极限定理。