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2009 Moment identities for Skorohod integrals on the Wiener space and applications
Nicolas Privault
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Electron. Commun. Probab. 14: 116-121 (2009). DOI: 10.1214/ECP.v14-1450


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.


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Nicolas Privault. "Moment identities for Skorohod integrals on the Wiener space and applications." Electron. Commun. Probab. 14 116 - 121, 2009.


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

zbMATH: 1189.60113
MathSciNet: MR2481671
Digital Object Identifier: 10.1214/ECP.v14-1450

Primary: 60H07
Secondary: 60G30

Keywords: Malliavin calculus , random isometries , Skorohod integral , Skorohod isometry , Wiener measure

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