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

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Functional Central Limit Theorems for Occupancies and Missing Mass Process in Infinite Urn Models. / Chebunin, Mikhail; Zuyev, Sergei.

In: Journal of Theoretical Probability, Vol. 35, No. 1, 03.2022.

Research output: Contribution to journal › Article › peer-review

BibTeX

@article{0295c7c1d82a40b7a0e8fa5305168d71,

title = "Functional Central Limit Theorems for Occupancies and Missing Mass Process in Infinite Urn Models",

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.",

keywords = "Functional CLT, Infinite urn scheme, Missing mass process, Occupancy process, Regular variation, SCHEME, COUNTS",

author = "Mikhail Chebunin and Sergei Zuyev",

note = "Funding Information: MC{\textquoteright}s research was supported by RSF Grant 17-11-01173-Ext. He also acknowledges hospitality of Chalmers University where a part of this work has been done. The authors are thankful to Sergey Foss for his interest in this research and valuable comments and to the anonymous reviewer for thorough reading and spotting some inaccuracies in the previous version of the manuscript. Publisher Copyright: {\textcopyright} 2020, The Author(s). Copyright: Copyright 2020 Elsevier B.V., All rights reserved.",

year = "2022",

month = mar,

doi = "10.1007/s10959-020-01053-6",

language = "English",

volume = "35",

journal = "Journal of Theoretical Probability",

issn = "0894-9840",

publisher = "Springer New York",

number = "1",

}

RIS

TY - JOUR

T1 - Functional Central Limit Theorems for Occupancies and Missing Mass Process in Infinite Urn Models

AU - Chebunin, Mikhail

AU - Zuyev, Sergei

N1 - Funding Information: MC’s research was supported by RSF Grant 17-11-01173-Ext. He also acknowledges hospitality of Chalmers University where a part of this work has been done. The authors are thankful to Sergey Foss for his interest in this research and valuable comments and to the anonymous reviewer for thorough reading and spotting some inaccuracies in the previous version of the manuscript. Publisher Copyright: © 2020, The Author(s). Copyright: Copyright 2020 Elsevier B.V., All rights reserved.

PY - 2022/3

Y1 - 2022/3

N2 - 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.

AB - 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.

KW - Functional CLT

KW - Infinite urn scheme

KW - Missing mass process

KW - Occupancy process

KW - Regular variation

KW - SCHEME

KW - COUNTS

UR - http://www.scopus.com/inward/record.url?scp=85096433425&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/755c4e98-6016-340b-aded-8ffe216fd977/

U2 - 10.1007/s10959-020-01053-6

DO - 10.1007/s10959-020-01053-6

M3 - Article

AN - SCOPUS:85096433425

VL - 35

JO - Journal of Theoretical Probability

JF - Journal of Theoretical Probability

SN - 0894-9840

IS - 1

ER -

ID: 26135569