Multiplicative monotone convolutions

Details Multiplicative monotone convolutions Multiplicative monotone convolutions

2005-03-25

arxiv.org/abs/math/0503602v1

Banach Center Publ. 73 (2006), 153-166

Mathematics

Probability

14 pages

Scientific paper

Recently, Bercovici has introduced multiplicative convolutions based on Muraki's monotone independence and shown that these convolution of probability measures correspond to the composition of some function of their Cauchy transforms. We provide a new proof of this fact based on the combinatorics of moments. We also give a new characterisation of the probability measures that can be embedded into continuous monotone convolution semigroups of probability measures on the unit circle and briefly discuss a relation to Galton-Watson processes.

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