Electronic Communications in Probability

Moment identities for Skorohod integrals on the Wiener space and applications

Nicolas Privault

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We prove a moment identity on the Wiener space that extends the Skorohod isometry to arbitrary powers of the Skorohod integral on the Wiener space. As simple consequences of this identity we obtain sufficient conditions for the Gaussianity of the law of the Skorohod integral and a recurrence relation for the moments of second order Wiener integrals. We also recover and extend the sufficient conditions for the invariance of the Wiener measure under random rotations given in A. S. Üstünel and M. Zakai Prob. Th. Rel. Fields 103 (1995), 409-429.

Article information

Electron. Commun. Probab., Volume 14 (2009), paper no. 11, 116-121.

Accepted: 19 February 2009
First available in Project Euclid: 6 June 2016

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Zentralblatt MATH identifier

Primary: 60H07: Stochastic calculus of variations and the Malliavin calculus
Secondary: 60G30: Continuity and singularity of induced measures

Malliavin calculus Skorohod integral Skorohod isometry Wiener measure random isometries

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Privault, Nicolas. Moment identities for Skorohod integrals on the Wiener space and applications. Electron. Commun. Probab. 14 (2009), paper no. 11, 116--121. doi:10.1214/ECP.v14-1450. https://projecteuclid.org/euclid.ecp/1465234720

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