Comptes Rendus
Probability Theory
Some remarks about the positivity of random variables on a Gaussian probability space
[Quelques remarques sur la positivité des variables aléatoires définies sur un espace gaussien.]
Comptes Rendus. Mathématique, Volume 339 (2004) no. 12, pp. 873-877.

Soit (W,H,μ) un espace de Wiener abstrait et soit LLlogL une variable aléatoire positive. A l'aide de la théorie de transport de mesure de Monge–Kantorovitch, nous montrons que le noyau de la projection de L dans le second chaos de Wiener est un opérateur de spectre inférieurement borné et que l'opérateur correspondant est inférieurement borné par un opérateur Hilbert–Schmidt semi-positif.

Let (W,H,μ) be an abstract Wiener space and let LLlogL(μ) is a positive random variable. Using the measure transportation of Monge–Kantorovitch, we prove that the operator corresponding to the kernel of the projection of L on the second Wiener chaos is lower bounded by a semi-positive Hilbert–Schmidt operator.

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DOI : 10.1016/j.crma.2004.10.014

Denis Feyel 1 ; A. Suleyman Üstünel 2

1 Université d'Evry-Val-d'Essone, département de mathématiques, 91025 Evry cedex, France
2 ENST, département Infres, 46, rue Barrault, 75013 Paris, France
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Denis Feyel; A. Suleyman Üstünel. Some remarks about the positivity of random variables on a Gaussian probability space. Comptes Rendus. Mathématique, Volume 339 (2004) no. 12, pp. 873-877. doi : 10.1016/j.crma.2004.10.014. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2004.10.014/

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