We investigate a probabilistic interpretation of the Wick product associated to the chisquare distribution in the spirit of the results obtained in Ref. 7 for the Gaussian measure. Our main theorem points out a profound difference from the previously studied Gaussian7 and Poissonian12 cases. As an application, we obtain a Young-type inequality for the Wick product associated to the chi-square distribution which contains as a particular case a known Nelson-type hypercontractivity theorem.
Lanconelli A, Sportelli L (2012). Wick calculus for the square of a Gaussian random variable with application to Young and hypercontractive inequalities. INFINITE DIMENSIONAL ANALYSIS QUANTUM PROBABILITY AND RELATED TOPICS, 15(3), 1-16 [10.1142/S021902571250018X].
Wick calculus for the square of a Gaussian random variable with application to Young and hypercontractive inequalities
Lanconelli A
Investigation
;
2012
Abstract
We investigate a probabilistic interpretation of the Wick product associated to the chisquare distribution in the spirit of the results obtained in Ref. 7 for the Gaussian measure. Our main theorem points out a profound difference from the previously studied Gaussian7 and Poissonian12 cases. As an application, we obtain a Young-type inequality for the Wick product associated to the chi-square distribution which contains as a particular case a known Nelson-type hypercontractivity theorem.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
