Simple Random Measure and Simple Processes

A simple random measure is a finite sums of random measures with disjoint supports. A type of simple random measures which is induced by a multivariate random measure (Φ1,…, Φm) and measurable mappings T1 ,…, Tm are introduced and studied. Interestingly it gives rise to introducing a class of processes, called simple, that include stationary and discrete time Periodically correlated processes. This study involves spectral domain and time domain characterizations and simulation. The role of spectral kernel in study of non-stationary processes are also brought into site.

Keywords:

Random Measure , Simple Random Measure , Simple processes , Cholesky Decomposition , Spectral kernel , Spectral Domain , Time Domain , Simulation.