Let (B) be a Brownian motion and let (widehat{B}_{t}=B_{t}-int_{0}^{t} d s frac{B_{s}}{s}). Prove that for every (t),
Question:
Let \(B\) be a Brownian motion and let \(\widehat{B}_{t}=B_{t}-\int_{0}^{t} d s \frac{B_{s}}{s}\).
Prove that for every \(t\), the r.v's \(B_{t}\) and \(\widehat{B}_{t}\) are not correlated, hence are independent. However, clearly, the two Brownian motions \(B\) and \(\widehat{B}\) are not independent. There is no contradiction with our previous discussion, as \(\widehat{B}\) is not an \(\mathbf{F}^{B}\)-Brownian motion.
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To prove that for every t the random variables Bt and widehatBt are not correlated we first need to ...View the full answer
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Related Book For 
Mathematical Methods For Financial Markets
ISBN: 9781447125242
1st Edition
Authors: Monique Jeanblanc, Marc Yor, Marc Chesney
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