I am trying to compute the asymptotic variance of OU process $$ d X_t = - H X_t dt + S dW_t $$ where $X_t$ takes value in $R^d$. $H$ and $S$ are $d\times d$ matrices that does not have $HS = SH$ in general. How to compute its variance at $t$?
Things are classical for one dimensional case as $$ Var (X_t) = \sigma^2 / \mu (1-e^{-\mu t}) $$