A limit theorem for the q-convolution

• Autorzy: Anna Kula
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 42A85: Convolution, factorization
• 60F05: Central limit and other weak theorems
• 28D05: Measure-preserving transformations
• 44A60: Moment problems

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2011
• Tom: 96
• Numer: 1
• Strony: 245-255

Daty

wydano

2011

Twórcy

autor

Anna Kula

• Institute of Mathematics, Jagiellonian University, ul. S. Łojasiewicza 6, 30-348 Kraków, Poland

Identyfikatory

DOI

10.4064/bc96-0-16