Remarks on t-transformations of measures and convolutions

A family of transformations of probability measures is constructed, and used to define transformations of convolutions. The relations between moments and cumulants of a measure and its transformation are presented. For transformed classical and free convolutions the central lit-nit measures and the Poisson type limit measures are computed. Families of non-commutative random variables are constructed, which are associated to these central limit measures. They provide examples of "position operators" which act on the Interacting Fock Spaces. (C) 2001 Editions scientifiques et medicales Elsevier SAS.