Electronic Communications in Probability

Moment identities for Skorohod integrals on the Wiener space and applications

Nicolas Privault

Abstract

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

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

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

https://projecteuclid.org/euclid.ecp/1465234720

Digital Object Identifier
doi:10.1214/ECP.v14-1450

Mathematical Reviews number (MathSciNet)
MR2481671

Zentralblatt MATH identifier
1189.60113

Rights