Functional Central Limit Theorems for Occupancies and Missing Mass Process in Infinite Urn Models

Mikhail Chebunin, Sergei Zuyev

Research output: Contribution to journalArticlepeer-review

Abstract

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 pj, where ∑ jpj= 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.

Original languageEnglish
Number of pages19
JournalJournal of Theoretical Probability
DOIs
Publication statusPublished - 23 Nov 2020

Keywords

  • Functional CLT
  • Infinite urn scheme
  • Missing mass process
  • Occupancy process
  • Regular variation
  • SCHEME
  • COUNTS

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