Let \(B_t\) and \(W_t\) be standard Brownian motions which are

independent. Consider

\begin{align*}

dX_t&= (-X_t +1)dt + \rho dB_t + \sqrt{1-\rho^2} dW_t\\

dY_t&= -Y_t dt + dB_t \ .

\end{align*}

Find the covariance of \(\text{Cov}(X_t,Y_t)=\mathbf{E} (X_t Y_t) – \mathbf{E} (X_t) \mathbf{E}( Y_t)\).

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