The invertibility of adapted perturbations of identity on the Wiener space

A. Suleyman Üstünel; Moshe Zakai

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

A. Suleyman Üstünel ¹ ; Moshe Zakai 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, Volume 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 :

A. Suleyman Üstünel ¹ ; Moshe Zakai 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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     author = {A. Suleyman \"Ust\"unel and Moshe Zakai},
     title = {The invertibility of adapted perturbations of identity on the {Wiener} space},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {689--692},
     publisher = {Elsevier},
     volume = {342},
     number = {9},
     year = {2006},
     doi = {10.1016/j.crma.2006.02.031},
     language = {en},
}

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A. Suleyman Üstünel; Moshe Zakai. The invertibility of adapted perturbations of identity on the Wiener space. Comptes Rendus. Mathématique, Volume 342 (2006) no. 9, pp. 689-692. doi : 10.1016/j.crma.2006.02.031. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2006.02.031/

Bibliographie
Cité par

[1] T. Carleman Zur Theorie der linearen Integralgleichungen, Math. Z., Volume 9 (1921), pp. 196-217

[2] N. Dunford; J.T. Schwartz Linear Operators, vol. 2, Interscience, New York, 1967

[3] D. Feyel; A. de La Pradelle Capacités gaussiennes, Ann. Inst. Fourier, Volume 41 (1991) no. 1, pp. 49-76

[4] P. Malliavin Stochastic Analysis, Springer, 1997

[5] A.S. Üstünel Introduction to Analysis on Wiener Space, Lecture Notes in Math., vol. 1610, Springer, 1995

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

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

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