# A limit theorem for the q-convolution

Banach Center Publications (2011)

- Volume: 96, Issue: 1, page 245-255
- ISSN: 0137-6934

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topAnna 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 -

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