SUBORDINATION OF STATIONARY PROCESSES

Abstract. Let X ={ X ( t ), t ε T ∁ R} be a ( L ₂ -) stationary process and suppose that N ={ N ( t ), t ≥ 0} is an infinitely divisible process, independent of X. Then ={ ( 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 .