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

TL;DR

This paper introduces a four-parameter family of covariance functions, called 2Dsys, for stationary Gaussian processes, derived from second-order stochastic differential equations, useful for modeling damped oscillations or overdamped systems.

Contribution

It presents a new, natural family of covariance functions based on second-order stochastic differential equations, expanding modeling options for stationary Gaussian processes.

Findings

Covers both underdamped and overdamped systems

Provides a natural solution derived from stochastic differential equations

Useful for distinguishing oscillatory from overdamped time-series

Abstract

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.