State-space representation of Matérn and Damped Simple Harmonic Oscillator Gaussian processes

Abstract: Gaussian processes (GPs) are used widely in the analysis of astronomical time series. GPs with rational spectral densities have state-space representations which allow O(n) evaluation of the likelihood. We calculate analytic state space representations for the damped simple harmonic oscillator and the Mat\'ern 1/2, 3/2 and 5/2 processes.