Prove Proposition 1 4 3 3 Proposition 1 4 3 3 Let (B t Gamma W t ) where (W ) is a d dimensional Brownian motion and ( Gamma left( gamma i, j ight) ) is a (d times d ) matrix with ( sum j 1 d gamma i, j 2 1 ) The process (B ) is a vector of correlated Brownian motions, with correlation matrix (ho G...

To prove Proposition 1433 we need to show that the process Bt Gamma Wt where W is a ddimensional Bro ...

Prove Proposition 1.4.3.3. Proposition 1.4.3.3: Let (B_{t}=Gamma W_{t}) where (W) is a d-dimensional Brownian motion and (Gamma=left(gamma_{i,

Question:

Prove Proposition 1.4.3.3.

Proposition 1.4.3.3:

Let $B_{t}=\Gamma W_{t}$ where $W$ is a d-dimensional Brownian motion and $\Gamma=\left(\gamma_{i, j}\right)$ is a $d \times d$ matrix with $\sum_{j=1}^{d} \gamma_{i, j}^{2}=1$. The process $B$ is a vector of correlated Brownian motions, with correlation matrix $ho=\Gamma \Gamma^{*}$.

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