Abstract
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 (Ω, ℬ, {ℱ t }0≤t≤T , P) and let be defined as , where u(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 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,
Mathematics Subject Classification:
The author wishes to express her thanks to Prof. Bernt Øksendal for suggestion of the problem and all the valuable comments.