New Examples of Convolutions and Non-Commutative Central Limit Theorems

• Autorzy: Marek Bożejko , Janusz Wysoczański
• Języki publikacji: EN

Abstrakty

EN

A family of transformations on the set of all probability measures on the real line is introduced, which makes it possible to define new examples of convolutions. The associated central limit theorems are studied, and examples of the limit measures, related to the classical, free and boolean convolutions, are shown.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 1998
• Tom: 43
• Numer: 1
• Strony: 95-103

Daty

wydano

1998

Twórcy

autor

Marek Bożejko

• Institute of Mathematics, University of Wrocław, pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland

autor

Janusz Wysoczański

• Institute of Mathematics, University of Wrocław, pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland

Bibliografia

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• [BSp1] M. Bożejko and R. Speicher, Interpolation between bosinic and fermionic relations given by generalized Brownian motions, Math. Z. 222 (1996), 135-160.
• [BSp2] M. Bożejko, B. Kümmerer and R. Speicher, q-Gaussian Processes: Non-commutative and Classical Aspects, Comm. Math. Phys. 185 (1997), 129-154.
• [Ma] H. Maassen, Addition of Freely Independent Random Variables, J. Funct. Anal. 106 No. 2 (1992), 409-438.
• [Sp] R. Speicher, Multiplicative functions on the lattice of non-crossing partitions and free convolution, Math. Ann. 298 (1994), 611-628.