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.
Wick calculus for the square of a Gaussian random variable with application to Young and hypercontractive inequalities / Lanconelli, A; Sportelli, L. - In: INFINITE DIMENSIONAL ANALYSIS QUANTUM PROBABILITY AND RELATED TOPICS. - ISSN 0219-0257. - 15:3(2012).
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Titolo: | Wick calculus for the square of a Gaussian random variable with application to Young and hypercontractive inequalities |
Autori: | |
Data di pubblicazione: | 2012 |
Rivista: | |
Citazione: | Wick calculus for the square of a Gaussian random variable with application to Young and hypercontractive inequalities / Lanconelli, A; Sportelli, L. - In: INFINITE DIMENSIONAL ANALYSIS QUANTUM PROBABILITY AND RELATED TOPICS. - ISSN 0219-0257. - 15:3(2012). |
Handle: | http://hdl.handle.net/11586/105799 |
Appare nelle tipologie: | 1.1 Articolo in rivista |