# Functional central limit theorems for occupancies and missing mass process in infinite urn models

## TL;DR

This paper establishes functional central limit theorems for occupancy and missing mass processes in infinite urn models, extending previous non-functional results to a more comprehensive probabilistic framework.

## Contribution

It introduces functional CLTs for both discrete and poissonized versions of the urn occupancy and missing mass processes, advancing the theoretical understanding of infinite urn schemes.

## Key findings

- Proves functional CLTs for occupancy processes
- Extends results to missing mass processes
- Includes both discrete and poissonized models

## Abstract

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