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 Electronic Communications in Probability > Vol. 14 (2009) > Paper 11 open journal systems 


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.


Full text: PDF

Pages: 116-121

Published on: February 19, 2009
Bibliography
  1. D. Nualart. The Malliavin calculus and related topics. Probability and its Applications, Springer-Verlag, Berlin, second edition, 2006. Math. Review 2006j:60004
  2. A.S. Üstünel and M. Zakai. Random rotations of the Wiener path. Prob. Th. Rel. Fields 103 (1995), 409-429. Math. Review 97a:60060
  3. A.V. Skorokhod. On a generalization of a stochastic integral. Theor. Probab. Appl. XX (1975), 219-223. Math. Review 52#12079
  4. S. Watanabe. Lectures on Stochastic Differential Equations and Malliavin Calculus. Tata Institute of Fundamental Research, 1984. Math. Review 86b:60113
















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Electronic Communications in Probability. ISSN: 1083-589X