  Recent work has addressed the problem of inferring Langevin dynamics from
data. In this work, we address the problem of relating terms in the Langevin
equation to statistical properties, such as moments of the probability density
function and of the probability current density, as well as covariance
functions. We first review the case of linear Gaussian dynamics, and then
consider extensions beyond this simple case. We address the question of
quantitative significance of effects. We also analyze underdamped
(second-order) processes, specifically in the limit where dynamics in state
space is almost Markovian. Finally, we address detection of non-Markovianity.
