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

Mikhail Chebunin () and Sergei Zuyev ()
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Mikhail Chebunin: Novosibirsk State University
Sergei Zuyev: Chalmers University of Technology

Journal of Theoretical Probability, 2022, vol. 35, issue 1, 1-19

Abstract: 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 $$p_j$$ p j , where $$\sum _j p_j=1$$ ∑ 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.

Keywords: Infinite urn scheme; Regular variation; Functional CLT; Occupancy process; Missing mass process; 60F17; 60G22; 60G15; 60G18 (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10959-020-01053-6

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