In the case that we are trying to solve the Sylvester/Lyapunov equation, $$BS + SB^{\top} = -kI$$ where $k$ is some constant positive value and $I$ is the identity, $S$ is a symmetric matrix and $B$ is a matrix - all matrices are square. is there a closed form solution for the symmetric matrix $S$? Note $B$ is not symmetric in general.
Context: the matrix $S$ represents the stationary covariance matrix of an OU-process with friction $B$ and uncorrelated, equal intensity noise terms.
