SUBORDINATION OF STATIONARY PROCESSES
Eric Willekens, Jef L. Teugels · Journal of Time Series Analysis · 1988
Abstract. Let X={X(t), tεT∁ R} be a (L2 ‐) stationary process and suppose that N={N(t), t≥ 0} is an infinitely divisible process, independent of X. Then X̂={X̂(t) =X(N(t)), t≥ 0} is again a stationary process. In this paper, we relate the spectral properties of the original process X and the derived or subordinated process X̂.