A hierarchical version of the de Finetti and Aldous-Hoover representations

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...

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Bibliographic Details
Published inProbability theory and related fields Vol. 159; no. 3-4; pp. 809 - 823
Main Authors Austin, Tim, Panchenko, Dmitry
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.08.2014
Springer Nature B.V
Subjects
Arrays
Economics
Exchange
Finance
Insurance
Invariants
Leaves
Management
Mathematical analysis
Mathematical and Computational Biology
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Parent-child relations
Preserves
Probability
Probability theory
Probability Theory and Stochastic Processes
Quantitative Finance
Random variables
Representations
Statistics for Business
Studies
Theorems
Theoretical
Trees
Spin glasses
60G09
60K35
Exchangeability
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Summary: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.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
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ISSN:0178-8051
1432-2064
DOI:10.1007/s00440-013-0521-0