Multiplicative monotone convolutions

• Autorzy: Uwe Franz
• Języki publikacji: EN

Abstrakty

EN

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.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2006
• Tom: 73
• Numer: 1
• Strony: 153-166

Daty

wydano

2006

Twórcy

autor

Uwe Franz

• Département de mathématiques de Besançon, Université de Franche-Comté, 16, route de Gray, 25 030 Besançon Cedex, France

Identyfikatory

DOI

10.4064/bc73-0-10