The invertibility of adapted perturbations of identity on the Wiener space

Üstünel, A. Suleyman; Zakai, Moshe

doi:10.1016/j.crma.2006.02.031

Probability Theory/Functional Analysis

The invertibility of adapted perturbations of identity on the Wiener space
[L'inversibilité des perturbations d'identité adaptées sur l'espace de Wiener]

Présenté par : Paul Malliavin

Üstünel, A. Suleyman ¹ ; Zakai, Moshe ²

¹ ENST – Paris, Département Infres, 46, rue Barrault, 75013 Paris, France
² Technion, Haifa, Department of Electrical Engineering, 32000 Haifa, Israel

Comptes Rendus. Mathématique, Tome 342 (2006) no. 9, pp. 689-692.

Résumé
Abstract

Soit $(W, H, μ)$ l'espace de Wiener. Soit $U = I_{W} + u$ une perturbation d'identité adaptée, i.e., $u : W \to H$ est adaptée à la filtration canonique de W. Nous donnons quelques conditions suffisantes qui impliquent l'inversibilité de l'application U.

Let $(W, H, μ)$ be the classical Wiener space. Assume that $U = I_{W} + u$ is an adapted perturbation of identity, i.e., $u : W \to H$ is adapted to the canonical filtration of W. We give some sufficient analytic conditions on u which imply the invertibility of the map U.

Reçu le : 2006-02-14
Accepté le : 2006-02-22
Publié le : 2006-03-29

DOI : 10.1016/j.crma.2006.02.031

Affiliations des auteurs :

Üstünel, A. Suleyman ¹ ; Zakai, Moshe ²

¹ ENST – Paris, Département Infres, 46, rue Barrault, 75013 Paris, France
² Technion, Haifa, Department of Electrical Engineering, 32000 Haifa, Israel

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     title = {The invertibility of adapted perturbations of identity on the {Wiener} space},
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Üstünel, A. Suleyman; Zakai, Moshe. The invertibility of adapted perturbations of identity on the Wiener space. Comptes Rendus. Mathématique, Tome 342 (2006) no. 9, pp. 689-692. doi : 10.1016/j.crma.2006.02.031. http://www.numdam.org/articles/10.1016/j.crma.2006.02.031/

Bibliographie
Cité par

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[6] Üstünel, A.S. Analysis on Wiener space and applications http://www.finance-research.net/ (Electronic text at the site)

[7] Üstünel, A.S.; Zakai, M. Transformation of Measure on Wiener Space, Springer-Verlag, 1999

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