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2019 Characteristic functionals of Dirichlet measures
Lorenzo Dello Schiavo
Electron. J. Probab. 24: 1-38 (2019). DOI: 10.1214/19-EJP371

Abstract

We compute the characteristic functional of the Dirichlet–Ferguson measure over a locally compact Polish space and prove continuous dependence of the random measure on the parameter measure. In finite dimension, we identify the dynamical symmetry algebra of the characteristic functional of the Dirichlet distribution with a simple Lie algebra of type $A$. We study the lattice determined by characteristic functionals of categorical Dirichlet posteriors, showing that it has a natural structure of weight Lie algebra module and providing a probabilistic interpretation. A partial generalization to the case of the Dirichlet–Ferguson measure is also obtained.

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Lorenzo Dello Schiavo. "Characteristic functionals of Dirichlet measures." Electron. J. Probab. 24 1 - 38, 2019. https://doi.org/10.1214/19-EJP371

Information

Received: 19 March 2019; Accepted: 4 October 2019; Published: 2019
First available in Project Euclid: 11 October 2019

zbMATH: 07142909
MathSciNet: MR4029418
Digital Object Identifier: 10.1214/19-EJP371

Subjects:
Primary: 60E10
Secondary: 33C65, 33C67, 46F25, 60G57, 62E10

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