Representation of strongly harmonizable periodically correlated processes and their covariances (Q581923)

This paper discusses the representation of continuous-time strongly harmonizable periodically correlated processes and their covariance functions. It contains several nice results of which two are stated here. 1) It is shown that the 2-dimensional spectral measure of such processes are concentrated on a set of equally spaced lines parallel to the main diagonal. 2) It is proved that any continuous-time strongly harmonizable periodically correlated process with period T may be represented, in quadratic mean as \[ X_ t=\sum_{k}a_ k(t)\exp (i2\pi Kt/T), \] where \(a_ k(t)\), \(-\infty <t<\infty\), \(-\infty <k<\infty\), are stationary and stationary correlated processes with specific covariance and cross covariance functions.