In the proof of Theorem 14.2 we assume that \(\left(B_{t}ight)_{t \geqslant 0}\) and \((U, W)\) are independent. Show that \(\mathscr{F}_{t}:=\sigma\left(B_{s}, s \leqslant t ; U, Wight)\) is an admissible filtration for a Brownian motion, cf. Definition 5.1.

Data From Theorem 14.2

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14.2 Theorem (Skorokhod 1965). Let X be a real random variable with distribution Ex. 14.2 function F. If E|X| 0: B(t) & (U, W)}, (U,W)