Publication: Free completely random measures
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2011-07
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Abstract
Free probability is a noncommutative probability theory introduced by Voiculescu
where the concept of independence
of classical probability is replaced by the concept of freeness. An important connection
between free and classical
infinite divisibility was established by Bercovici and Pata (1999) in form of a bijection,
mapping the class of classical
infinitely divisible laws into the class of free infinitely divisible laws.
A particular class of infinitely divisible laws are the completely random measures
introduced by Kingman (1967). In
this paper, a free analogous of completely random measures is introduced and, a free
Poisson process characterization
is provided as well as a representation through a free cumulant transform. Furthermore,
some examples are displayed.
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Bayesian non parametrics, Bercovici-Pata bijection, Free completely random measures, Free infinite divisibility, Free probability