Simple random measures and simple processes

A simple random measure is a finite sum of random measures with disjoint supports. A type of simple random measure which is induced by a multivariate random measure $(\Phi_1,\dots,\Phi_m)$ and measurable mappings $T_1,\dots,T_m$ is introduced and studied. Interestingly it gives rise to introducing a class of processes, called simple, that include stationary processes and discrete time periodically correlated processes. This study involves spectral domain and time domain characterizations and simulation. The role of spectral kernels in analysis of nonstationary processes is also discussed.