[Quelques remarques sur la positivité des variables aléatoires définies sur un espace gaussien.]
Soit un espace de Wiener abstrait et soit 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 be an abstract Wiener space and let 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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@article{CRMATH_2004__339_12_873_0,
author = {Feyel, Denis and \"Ust\"unel, A. Suleyman},
title = {Some remarks about the positivity of random variables on a {Gaussian} probability space},
journal = {Comptes Rendus. Math\'ematique},
pages = {873--877},
publisher = {Elsevier},
volume = {339},
number = {12},
year = {2004},
doi = {10.1016/j.crma.2004.10.014},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2004.10.014/}
}
TY - JOUR AU - Feyel, Denis AU - Üstünel, A. Suleyman TI - Some remarks about the positivity of random variables on a Gaussian probability space JO - Comptes Rendus. Mathématique PY - 2004 SP - 873 EP - 877 VL - 339 IS - 12 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2004.10.014/ DO - 10.1016/j.crma.2004.10.014 LA - en ID - CRMATH_2004__339_12_873_0 ER -
%0 Journal Article %A Feyel, Denis %A Üstünel, A. Suleyman %T Some remarks about the positivity of random variables on a Gaussian probability space %J Comptes Rendus. Mathématique %D 2004 %P 873-877 %V 339 %N 12 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2004.10.014/ %R 10.1016/j.crma.2004.10.014 %G en %F CRMATH_2004__339_12_873_0
Feyel, Denis; Üstünel, A. Suleyman. Some remarks about the positivity of random variables on a Gaussian probability space. Comptes Rendus. Mathématique, Tome 339 (2004) no. 12, pp. 873-877. doi : 10.1016/j.crma.2004.10.014. http://www.numdam.org/articles/10.1016/j.crma.2004.10.014/
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