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# 9. [10] Suppose that B and W are BMs and that they are correlated with correlation coefficient P (-1, 1) in the sense that

## 9. [10] Suppose that B and W are BMs and that they are correlated with correlation coefficient P (-1, 1) in the sense that the correlation coefficient between Bt and Wt for all t>0. Then we can decompose W as is Wt = aWt+bBt, t 0, where (i) a, b = R and (ii) is a BM uncorrelated with B (in the sense that the correlation coefficient between W and Bt is zero for all t > 0). Find the values of a and b that work. (You do not need to show (i) and (ii). Simply assume them, and find the right values of a and b. If you remember the answer, write that down and verify it satisfies (ii).)

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constants a and b such that W t aW t bB t Given that B t and areW t Brownian motions BMs with correl...### Get Instant Access to Expert-Tailored Solutions

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