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

2019/06/26 by Mikhail Chebunin, Chebunin, Mikhail, Sergei Zuyev +1
Mathematics · #60F17 #60G22 #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Mathematical Dynamics and Fractals #Probability (math.PR) #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1906.10949

openalex publication_date 2019/06/26 · openalex created_date 2022/07/28 · openalex updated_date 2026/07/28

Abstract

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

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