A hierarchical version of the de Finetti and Aldous-Hoover representations
成果类型：
Article
署名作者：
Austin, Tim; Panchenko, Dmitry
署名单位：
New York University; Texas A&M University System; Texas A&M University College Station
刊物名称：
PROBABILITY THEORY AND RELATED FIELDS
ISSN/ISSBN：
0178-8051
DOI：
10.1007/s00440-013-0521-0
发表日期：
2014
页码：
809-823
关键词：
摘要：
We consider random arrays indexed by the leaves of an infinitary rooted tree of finite depth, with the distribution invariant under the rearrangements that preserve the tree structure. We call such arrays hierarchically exchangeable and prove that they satisfy an analogue of de Finetti's theorem. We also prove a more general result for arrays indexed by several trees, which includes a hierarchical version of the Aldous-Hoover representation.
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