Auto and cross correlated random sequences

I'd like to generate two random sequences, X and Y,

X = x_1, x_2, x_3, ....., x_n
Y = y_1, y_2, y_3, ....., y_n

such that
corr(x_i, x_i+1) = rho_x
corr(y_i, y_i+1) = rho_y
corr(x_i, y_i) = rho_xy

If rho_x = rho_y =0, its easy - just generate two independent random
sequences U and V and then transform them into X and Y by
postmultiplying [U V] by the Cholesky decomposition of the covariance
matrix.

Question: How do I generate random variates that satisfy these 3
conditions when rho_x != 0, rho_y !=0, rho_xy !=0.

Thanks in advance

Thomas Philips

.

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