On the embeddability of certain infinitely divisible probability measures on Lie groups

We describe certain sufficient conditions for an infinitely divisible probability measure on a Lie group to be embeddable in a continuous one-parameter semigroup of probability measures. A major class of Lie groups involved in the analysis consists of central extensions of almost algebraic groups by...

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Bibliographic Details
Published in:Mathematische Zeitschrift 2012-10, Vol.272 (1-2), p.361-379
Main Authors: Dani, S. G., Guivarc’h, Yves, Shah, Riddhi
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
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Summary:We describe certain sufficient conditions for an infinitely divisible probability measure on a Lie group to be embeddable in a continuous one-parameter semigroup of probability measures. A major class of Lie groups involved in the analysis consists of central extensions of almost algebraic groups by compactly generated abelian groups without vector part. This enables us in particular to conclude the embeddability of all infinitely divisible probability measures on certain connected Lie groups, including the so called Walnut group. The embeddability is concluded also under certain other conditions. Our methods are based on a detailed study of actions of certain nilpotent groups on special spaces of probability measures and on Fourier analysis along the fibering of the extension.
ISSN:0025-5874
1432-1823
DOI:10.1007/s00209-011-0937-0