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

Author

Listed:
  • Mikhail Chebunin

    (Novosibirsk State University)

  • Sergei Zuyev

    (Chalmers University of Technology)

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.

Suggested Citation

  • Mikhail Chebunin & Sergei Zuyev, 2022. "Functional Central Limit Theorems for Occupancies and Missing Mass Process in Infinite Urn Models," Journal of Theoretical Probability, Springer, vol. 35(1), pages 1-19, March.
    • Handle: RePEc:spr:jotpro:v:35:y:2022:i:1:d:10.1007_s10959-020-01053-6
    DOI: 10.1007/s10959-020-01053-6
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    References listed on IDEAS

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    1. Chebunin, Mikhail & Kovalevskii, Artyom, 2016. "Functional central limit theorems for certain statistics in an infinite urn scheme," Statistics & Probability Letters, Elsevier, vol. 119(C), pages 344-348.
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    Cited by:

    1. Iksanov, Alexander & Kotelnikova, Valeriya, 2022. "Small counts in nested Karlin’s occupancy scheme generated by discrete Weibull-like distributions," Stochastic Processes and their Applications, Elsevier, vol. 153(C), pages 283-320.

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