A Clark-ocone Formula in Umd Banach Spaces
نویسندگان
چکیده
Let H be a separable real Hilbert space and let F = (Ft)t∈[0,T ] be the augmented filtration generated by an H-cylindrical Brownian motion (WH(t))t∈[0,T ] on a probability space (Ω,F ,P). We prove that if E is a UMD Banach space, 1 ≤ p < ∞, and F ∈ D(Ω;E) is FT -measurable, then F = E(F ) + ∫ T 0 PF(DF ) dWH , where D is the Malliavin derivative of F and PF is the projection onto the F-adapted elements in a suitable Banach space of L-stochastically integrable L (H,E)-valued processes.
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