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

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...

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Bibliographic Details
Published in:Österreichische Zeitschrift für Statistik Vol. 52; no. SI; pp. 1 - 12
Main Authors: Braganets, Oksana, Iksanov, Alexander
Format: Journal Article
Language:English
Published: Austrian Statistical Society 15-08-2023
Online Access:Get full text
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Summary: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.
ISSN:1026-597X
DOI:10.17713/ajs.v52iSI.1749