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D. Nualart (1991)
Nonlinear Transformations of the Wiener Measure and Applications
D. Nualart (1991)
Stochastic Analysis
G. Johnson, G. Kallianpur, Robert Cameron (1993)
Homogeneous chaos, p-forms, scaling and the Feynman integralTransactions of the American Mathematical Society, 340
L. Gross (1960)
Integration and non-linear transformations in Hilbert space
G. Kallianpur (1979)
Stochastic filtering theoryAdvances in Applied Probability, 11
T. Kailath, D. Duttweiler (1972)
An RKHS approach to detection and estimation problems- III: Generalized innovations representations and a likelihood-ratio formulaIEEE Trans. Inf. Theory, 18
R. Cameron, W. Martin (1949)
The transformation of Wiener integrals by nonlinear transformationsTransactions of the American Mathematical Society, 66
A. Üstünel, M. Zakai (1992)
Transformation of Wiener measure under anticipative flowsProbability Theory and Related Fields, 93
S. Kusuoka (1982)
The nonlinear transformation of Gaussian measure on Banach space and its absolute continuity (II)Journal of the Faculty of Science, the University of Tokyo. Sect. 1 A, Mathematics, 30
G. Kallianpur, R. Karandikar (1988)
White Noise Theory of Prediction, Filtering and Smoothing
C. Dellacherie, P. Meyer (1978)
Probabilities and potential C
R. Buckdahn (1991)
Anticipative Girsanov transformationsProbability Theory and Related Fields, 89
J. Feldman (1958)
Equivalence and perpendicularity of Gaussian processesPacific Journal of Mathematics, 8
Roald Ramer (1974)
On nonlinear transformations of Gaussian measuresJournal of Functional Analysis, 15
G. Kallianpur, H. Oodaira (1973)
Non-Anticipative Representations of Equivalent Gaussian ProcessesAnnals of Probability, 1
The papers of R. Ramer and S. Kusuoka investigate conditions under which the probability measure induced by a nonlinear transformation on abstract Wiener space(γ,H,B) is absolutely continuous with respect to the abstract Wiener measureμ. These conditions reveal the importance of the underlying Hilbert spaceH but involve the spaceB in an essential way. The present paper gives conditions solely based onH and takes as its starting point, a nonlinear transformationT=I+F onH. New sufficient conditions for absolute continuity are given which do not seem easily comparable with those of Kusuoka or Ramer but are more general than those of Buckdahn and Enchev. The Ramer-Itô integral occurring in the expression for the Radon-Nikodym derivative is studied in some detail and, in the general context of white noise theory it is shown to be an anticipative stochastic integral which, under a stronger condition on the weak Gateaux derivative of F is directly related to the Ogawa integral.
Acta Applicandae Mathematicae – Springer Journals
Published: Dec 31, 2004
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