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

被引：5

作者：

Chebunin, Mikhail ^{[1
]}

Zuyev, Sergei ^{[2
]}

机构：

[1] Novosibirsk State Univ, SB RAS, Sobolev Inst Math, Novosibirsk, Russia

[2] Chalmers Univ Technol, Gothenburg, Sweden

来源：

JOURNAL OF THEORETICAL PROBABILITY | 2022年 / 35卷 / 01期

关键词：

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

D O I：

10.1007/s10959-020-01053-6

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

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), where Sigma(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.

引用

页码：1 / 19

页数：19

共 4 条

[1] Functional Central Limit Theorems for Occupancies and Missing Mass Process in Infinite Urn Models
Mikhail Chebunin
Sergei Zuyev
Journal of Theoretical Probability, 2022, 35 : 1 - 19
[2] Functional central limit theorems for certain statistics in an infinite urn scheme
Chebunin, Mikhail
Kovalevskii, Artyom
STATISTICS & PROBABILITY LETTERS, 2016, 119 : 344 - 348
[3] Concentration inequalities in the infinite urn scheme for occupancy counts and the missing mass, with applications
Ben-Hamou, Anna
Boucheron, Stephane
Ohannessian, Mesrob I.
BERNOULLI, 2017, 23 (01) : 249 - 287
[4] Functional central limit theorems for rough volatility
Horvath, Blanka
Jacquier, Antoine
Muguruza, Aitor
Sojmark, Andreas
FINANCE AND STOCHASTICS, 2024, 28 (03) : 615 - 661

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