A limit theorem for the q-convolution

Anna Kula. "A limit theorem for the q-convolution." Banach Center Publications 96.1 (2011): 245-255. <http://eudml.org/doc/281594>.

@article{AnnaKula2011,
abstract = {The q-convolution is a measure-preserving transformation which originates from non-commutative probability, but can also be treated as a one-parameter deformation of the classical convolution. We show that its commutative aspect is further certified by the fact that the q-convolution satisfies all of the conditions of the generalized convolution (in the sense of Urbanik). The last condition of Urbanik's definition, the law of large numbers, is the crucial part to be proved and the non-commutative probability techniques are used.},
author = {Anna Kula},
journal = {Banach Center Publications},
keywords = {convolution; generalized convolution; moment sequence; law of large numbers},
language = {eng},
number = {1},
pages = {245-255},
title = {A limit theorem for the q-convolution},
url = {http://eudml.org/doc/281594},
volume = {96},
year = {2011},
}

TY - JOUR
AU - Anna Kula
TI - A limit theorem for the q-convolution
JO - Banach Center Publications
PY - 2011
VL - 96
IS - 1
SP - 245
EP - 255
AB - The q-convolution is a measure-preserving transformation which originates from non-commutative probability, but can also be treated as a one-parameter deformation of the classical convolution. We show that its commutative aspect is further certified by the fact that the q-convolution satisfies all of the conditions of the generalized convolution (in the sense of Urbanik). The last condition of Urbanik's definition, the law of large numbers, is the crucial part to be proved and the non-commutative probability techniques are used.
LA - eng
KW - convolution; generalized convolution; moment sequence; law of large numbers
UR - http://eudml.org/doc/281594
ER -