Selfdecomposable Measures on Simply Connected Nilpotent Groups

Riddhi Shah

Journal of Theoretical Probability, 2000, vol. 13, issue 1, 65-83

Abstract: Abstract The concepts of class L measures and selfdecomposable measures are generalised from vector spaces to simply connected nilpotent groups G. It has been shown that any full class L (probability) measure μ on G can be decomposed as μ = μ 1* ... *μ n, where each μ i is a selfdecomposable measure on a subgroup G i; μ itself is selfdecomposable under certain additional conditions—for example, when μ is symmetric. This generalizes a well known result on vector spaces. Some examples of class L measures on G are also constructed.

Keywords: nilpotent groups; convolution product of probability measures; selfdecomposable measures (search for similar items in EconPapers)
Date: 2000
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DOI: 10.1023/A:1007778725065

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