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

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2010-01-01
Okur, Yeliz Yolcu
We prove the white noise generalization of the Clark-Ocone formula under change of measure by using Gaussian white noise analysis and Malliavin calculus. Let W(t) be a Brownian motion on the filtered white noise probability space (Omega, B, {F(t)}(0 <= t <= T), P) and let (W) over cap (t) be defined as d (W) over cap (t) = u(t)dt + dW (t), where u W(t) is an F(t)-measurable process satisfying certain conditions for all 0 <= t <= T. Let Q be the probability measure equivalent to P such that (W) over cap is a Brownian motion with respect to Q, in virtue of the Girsanov theorem. In this article, it is shown that for any square integrable F(T)-measurable random variable,