Multiplicative monotone convolutions

Uwe Franz. "Multiplicative monotone convolutions." Banach Center Publications 73.1 (2006): 153-166. <http://eudml.org/doc/282155>.

@article{UweFranz2006,
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.},
author = {Uwe Franz},
journal = {Banach Center Publications},
keywords = {monotone independence; conditionally free product; Lévy–Khintchine formula},
language = {eng},
number = {1},
pages = {153-166},
title = {Multiplicative monotone convolutions},
url = {http://eudml.org/doc/282155},
volume = {73},
year = {2006},
}

TY - JOUR
AU - Uwe Franz
TI - Multiplicative monotone convolutions
JO - Banach Center Publications
PY - 2006
VL - 73
IS - 1
SP - 153
EP - 166
AB - 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.
LA - eng
KW - monotone independence; conditionally free product; Lévy–Khintchine formula
UR - http://eudml.org/doc/282155
ER -