  The linear Lyapunov equation of a covariance matrix parametrizes the
equilibrium covariance matrix of a stochastic process. This parametrization can
be interpreted as a new graphical model class, and we show how the model class
behaves under marginalization and introduce a method for structure learning via
$\ell_1$-penalized loss minimization. Our proposed method is demonstrated to
outperform alternative structure learning algorithms in a simulation study, and
we illustrate its application for protein phosphorylation network
reconstruction.
