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I'm really noob in maths topics so I hope you will excuse me if I use terms which aren't correct.

I would like to simulate $n$ dimensional diffusion processes with $n$ noises.

Each process has its variance and is correlated to others by correlation / covariance matrix.

My question is about the diffusion matrix: how is it linked to the correlation / covariance matrix?

Let I have martingales

$\begin{pmatrix} dX_{t}^{1}\\ dX_{t}^{2} \end{pmatrix} = 0+\begin{pmatrix} \cdots & \cdots \\ \cdots & \cdots \end{pmatrix}\begin{pmatrix} dW_{t}^{1}\\ dW_{t}^{2} \end{pmatrix}$.

What should I use instead of the empty diffusion matrix if my correlation / covariance matrix is like

$V=\begin{pmatrix} 1 & -.1\\ -.1 & 1 \end{pmatrix}$?

Thanks,

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