Moment identities for Skorohod integrals on the Wiener space and applications
Nicolas Privault, City University of Hong Kong
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.
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