Remarks on conditional moments of the free deformed Poisson random variables
Volume 96 / 2011
Banach Center Publications 96 (2011), 135-145
MSC: Primary 46L53, 46L54; Secondary 60E10.
DOI: 10.4064/bc96-0-8
Abstract
We will show that the conditional first moment of the free deformed Poisson random variables ($ q=0$) corresponding to operators fulfilling the free relation is a linear function of the regression and the conditional variance also is a linear function of the regression. For this purpose we will first demonstrate some properties of the Wick product and then we will concentrate on the free deformed Poisson random variables.
