A natural 4-parameter family of covariance functions for stationary Gaussian processes

A four-parameter family of covariance functions for stationary Gaussian processes is presented. We call it 2Dsys. It corresponds to the general solution of an autonomous second-order linear stochastic differential equation, thus arises naturally from modelling. It covers underdamped and overdamped systems, so it is proposed to use this family when one wishes to decide if a time-series corresponds to stochastically forced damped oscillations or a stochastically forced overdamped system.