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Comptes Rendus Mathématique
Volume 346, n° 15-16
pages 897-900 (août 2008)
Doi : 10.1016/j.crma.2008.07.013
Received : 7 July 2008 ;  accepted : 10 July 2008
A necessary and sufficient condition for invertibility of adapted perturbations of identity on Wiener space
Une condition nécessaire et suffisante pour lʼinversibilité de perturbations dʼidentité adaptées sur lʼespace de Wiener
 

A. Suleyman Üstünel
Telecom-Paristech, Département Infres, 46, rue Barrault, 75013 Paris, France 

Abstract

Let   be the classical Wiener space, assume that   is an adapted perturbation of identity satisfying the Girsanov identity. Then, U is invertible if and only if the kinetic energy of u is equal to the relative entropy of the measure induced with the action of U on the Wiener measure μ , in other words U is invertible if and only if
12∫W|u|H2dμ=∫WdUμdμlogdUμdμdμ. To cite this article: A.S. Üstünel, C. R. Acad. Sci. Paris, Ser. I 346 (2008).

The full text of this article is available in PDF format.
Résumé

Soit   lʼespace de Wiener classique, et soit   une perturbation dʼidentité adaptée satisfaisant á lʼidentité de Girsanov. Alors U est inversible si et seulement si lʼénergie cinétique de u est égale à lʼentropie relative de la mesure induite par lʼaction de U sur la mesure de Wiener μ ; en dʼautres termes U est inversible si et seulement si
12∫W|u|H2dμ=∫WdUμdμlogdUμdμdμ. Pour citer cet article : A.S. Üstünel, C. R. Acad. Sci. Paris, Ser. I 346 (2008).

The full text of this article is available in PDF format.


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