Embedding in law of discrete time ARMA processes in continuous time stationary processes

Given any stationary time series {Xn:n∈Z} satisfying an ARMA(p,q) model for arbitrary p and q with infinitely divisible innovations, we construct a continuous time stationary process {xt:t∈R} such that the distribution of {xn:n∈Z}, the process sampled at discrete time, coincides with the distribution of {Xn}. In particular the autocovariance function of {xt} interpolates that of {Xn}.