On nested infinite occupancy scheme in random environment

• 成果类型: Article
• 署名作者: Gnedin, Alexander; Iksanov, Alexander
• 署名单位: University of London; Queen Mary University London; Ministry of Education & Science of Ukraine; Taras Shevchenko National University of Kyiv
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-020-00963-0
• 发表日期: 2020
• 页码: 855-890
• 关键词: CENTRAL LIMIT-THEOREMS; regenerative compositions; asymptotic laws; stick-breaking; counts; number

摘要

We consider an infinite balls-in-boxes occupancy scheme with boxes organised in nested hierarchy, and random probabilities of boxes defined in terms of iterated fragmentation of a unit mass. We obtain a multivariate functional limit theorem for the cumulative occupancy counts as the number of balls approaches infinity. In the case of fragmentation driven by a homogeneous residual allocation model our result generalises the functional central limit theorem for the block counts in Ewens' and more general regenerative partitions.