Specifying general covariance to an ItoProcess?

I’m studying a system of stochastic equations and I would like to specify the covariance between the Wiener processes appearing in each. The Mathematica help’s page for ItoProcess indicates that this is possible, but does not make it clear how to indicate covariance.

For example, suppose I want to solve

$
qquad dx_1 = -gamma_1 x_1 dt + sigma_1 dW_1
qquad dx_2 = -gamma_2 x_2 dt + sigma_2 dW_2
$

where $dW_1$ and $dW_2$ are Wiener processes. Independently, this is easy since $x(t)$ and $y(t)$ are Ornstein Uhlenbeck processes, and Ito’s lemma gives $dW_1^2 = dW_2^2 = dt$. However, suppose they’re correlated such that $dW_1dW_2 = xi dt$ where $-1le xi le 1$?

How is this specified to ItoProcess?