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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc96-0-8,
author = {Wiktor Ejsmont},
title = {Remarks on conditional moments of the free deformed Poisson random variables},
journal = {Banach Center Publications},
volume = {95},
year = {2011},
pages = {135-145},
zbl = {1259.46053},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc96-0-8}
}
Wiktor Ejsmont. Remarks on conditional moments of the free deformed Poisson random variables. Banach Center Publications, Tome 95 (2011) pp. 135-145. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc96-0-8/