Comptes Rendus
Probability Theory/Functional Analysis
The invertibility of adapted perturbations of identity on the Wiener space
Comptes Rendus. Mathématique, Volume 342 (2006) no. 9, pp. 689-692.

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

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

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2006.02.031
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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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/

[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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