Stationary Covariance Generation with Finite State Markov Processes,

This paper studies the stationary covariance generation problem, i.e. the problem of passing from a stationary covariance function to a dynamical system which generates a process having the given covariance, in the case where the dynamical system is a finite state, continuous time, Markov process. Strictly positive definite stationary covariances can be approximated to any degree of accuracy in this way. However the number of states required may approach infinity as the covariance approaches the boundary of the set of positive definite functions.