随机环境下嵌套无限占用方案的极限定理

IF 0.6 Q4 STATISTICS & PROBABILITY

Austrian Journal of Statistics Pub Date : 2023-08-15 DOI:10.17713/ajs.v52isi.1749

Oksana Braganets, A. Iksanov

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引用次数: 0

摘要

我们研究了一种无限盒中球方案，其中盒子被安排在嵌套的层次结构中，盒子的随机概率被定义为单位质量的迭代碎片。Gnedin和Iksanov(2020)对球数变大时的累积占用数，得到了一个具有定心的多元泛函中心极限定理。我们证明了一个与他们的结果相对应的结果，其中不需要定心并且极限过程不是高斯的。给出了一个由剩余分配模型生成的方案的应用。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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A Limit Theorem for a Nested Infinite Occupancy Scheme in Random Environment

We investigate an infinite balls-in-boxes scheme, in which boxes are arranged in nested hierarchy and random probabilities of boxes are defined in terms of iterated fragmentation of a unit mass. Gnedin and Iksanov (2020) obtained a multivariate functional central limit theorem with centering for the cumulative occupancy counts as the number of balls becomes large. We prove a counterpart of their result, in which centering is not needed and the limit processes are not Gaussian. An application is given to the scheme generated by a residual allocation model.

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来源期刊

Austrian Journal of Statistics STATISTICS & PROBABILITY-

CiteScore

1.10

自引率

0.00%

发文量

审稿时长

24 weeks

期刊介绍： The Austrian Journal of Statistics is an open-access journal (without any fees) with a long history and is published approximately quarterly by the Austrian Statistical Society. Its general objective is to promote and extend the use of statistical methods in all kind of theoretical and applied disciplines. The Austrian Journal of Statistics is indexed in many data bases, such as Scopus (by Elsevier), Web of Science - ESCI by Clarivate Analytics (formely Thompson & Reuters), DOAJ, Scimago, and many more. The current estimated impact factor (via Publish or Perish) is 0.775, see HERE, or even more indices HERE. Austrian Journal of Statistics ISNN number is 1026597X Original papers and review articles in English will be published in the Austrian Journal of Statistics if judged consistently with these general aims. All papers will be refereed. Special topics sections will appear from time to time. Each section will have as a theme a specialized area of statistical application, theory, or methodology. Technical notes or problems for considerations under Shorter Communications are also invited. A special section is reserved for book reviews.