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White Noise Generalization of the Clark-Ocone Formula Under Change of Measure

2010
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Stochastic Analysis and Applications
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We prove white noise generalization of the Clark-Ocone formula under change of measure by using white noise analysis on Malliavin calculus. In this paper, it is shown that for any random variable F ∈ L 2 (P ) where E Q is the expectation under white noise measure Q,Ŵ (t) is the 1-dimensional Brownian motion constructed on the white noise probability space (Ω, B, Q) and D t F (ω) is the (Hida) Malliavin derivative. The important point to note here is in this settlement F should not belong to

doi:10.1080/07362994.2010.515498
fatcat:i4ysa57sb5e5hpxhun3avcxbsi