Let (left(B_{t} ight)_{t geqslant 0}) be a (mathrm{BM}^{1}) and (f in operatorname{BV}[0, T], T Data From 13.5

Let \(\left(B_{t}\right)_{t \geqslant 0}\) be a \(\mathrm{BM}^{1}\) and \(f \in \operatorname{BV}[0, T], T

Data From 13.5 Paragraph

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G (w) = $(s) dw(s) = (1)w(1) - [w(s) d(s), w C(o)[0, 1], 1)-\ - is well-defined. If we write G as the limit of a Riemann-Stieltjes sum, it is not hard to see that, on the Wiener space (e(o)[0, 1], B(C(o)[0, 1]), ), G is a normal random variable, mean 0, varlance [(s) ds; | G (w)G* (w)(dw) = [(s)(s) ds if , & BV[0, 1]. e(a) [0,1] (13.7a) (13.7b) Ex. 13.4