Remarks on conditional moments of the free deformed Poisson random variables

Volume 96 / 2011

Wiktor Ejsmont 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.

Authors

  • Wiktor EjsmontMathematical Institute, University of Wrocław
    pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland
    e-mail

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