Multiplicative monotone convolutions

Volume 73 / 2006

Uwe Franz Banach Center Publications 73 (2006), 153-166 MSC: Primary 46L50; Secondary 60E10. DOI: 10.4064/bc73-0-10

Abstract

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.

Authors

  • Uwe FranzDépartement de mathématiques de Besançon
    Université de Franche-Comté
    16, route de Gray,
    25 030 Besançon Cedex, France
    e-mail

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