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Contents of PMS, Vol. 24, Fasc. 1,
pages 97 - 119
 

GENERALIZED T -TRANSFORMATIONS OF PROBABILITY MEASURES AND DEFORMED CONVOLUTIONS

Anna Krystek
Hiroaki Yoshida

Abstract: In this paper, the generalized (two-parameterized) t -transformations on probability measures are introduced, in which the t -transformation of Bożejko and Wysoczański can be obtained as the special case, and the associated deformed convolutions are also investigated. We see that the generalized t -deformed free convolution can be realized as the conditionally free convolution of Bożejko, Leinert, and Speicher. We also study another special case of the generalized t -deformed free convolution, which is called the t -free convolution, that gives an interpolation between the free and the Fermi convolutions.

2000 AMS Mathematics Subject Classification: Primary 46L53, 46L54; Secondary 60E10.

Key words and phrases: Convolution, conditionally free, moment-cumulant formula.

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