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.
@article{arxiv.2109.10685,
title = {State-space representation of Mat\'ern and Damped Simple Harmonic Oscillator Gaussian processes},
author = {Andrés Jordán and Susana Eyheramendy and Johannes Buchner},
journal= {arXiv preprint arXiv:2109.10685},
year = {2021}
}