On some generalization of the t-transformation

Anna Dorota Krystek. "On some generalization of the t-transformation." Banach Center Publications 89.1 (2010): 165-187. <http://eudml.org/doc/282200>.

@article{AnnaDorotaKrystek2010,
abstract = {Using the Nevanlinna representation of the reciprocal of the Cauchy transform of probability measures, we introduce a two-parameter transformation $U^\{\}$ of probability measures on the real line ℝ, which is another possible generalization of the t-transformation. Using that deformation we define a new convolution by deformation of the free convolution. The central limit measure with respect to the -deformed free convolutions is still a Kesten measure, but the Poisson limit depends on the two parameters and is different from the Poisson measures for (a,b)-deformation. We also show that the -deformed free convolution is different from the convolution obtained as the deformed conditionally free convolution of Bożejko, Leinert and Speicher. Thus the does not satisfy the Bożejko property.},
author = {Anna Dorota Krystek},
journal = {Banach Center Publications},
keywords = {free convolution; conditionally free convolution; deformation; limit theorems; moment cumulant formulae},
language = {eng},
number = {1},
pages = {165-187},
title = {On some generalization of the t-transformation},
url = {http://eudml.org/doc/282200},
volume = {89},
year = {2010},
}

TY - JOUR
AU - Anna Dorota Krystek
TI - On some generalization of the t-transformation
JO - Banach Center Publications
PY - 2010
VL - 89
IS - 1
SP - 165
EP - 187
AB - Using the Nevanlinna representation of the reciprocal of the Cauchy transform of probability measures, we introduce a two-parameter transformation $U^{}$ of probability measures on the real line ℝ, which is another possible generalization of the t-transformation. Using that deformation we define a new convolution by deformation of the free convolution. The central limit measure with respect to the -deformed free convolutions is still a Kesten measure, but the Poisson limit depends on the two parameters and is different from the Poisson measures for (a,b)-deformation. We also show that the -deformed free convolution is different from the convolution obtained as the deformed conditionally free convolution of Bożejko, Leinert and Speicher. Thus the does not satisfy the Bożejko property.
LA - eng
KW - free convolution; conditionally free convolution; deformation; limit theorems; moment cumulant formulae
UR - http://eudml.org/doc/282200
ER -