Each stationary process can be biunivoquely associated with a random measure, through the Fourier transform. Consequently, every particularity of a process in the temporal domain has its corresponding one in the frequency domain. We propose to study the characteristics of the random measure when...

A Fubini-type formula for the integral with respect to the tensor product of two random measures is established in an intrinsic way. This permits one to consider a convolution product. The results are applied to a stationary continuous random function (which may be multiplicatively written with...

In this paper, we study how the local concentration of the spectral measure can be expressed in the temporal domain for stationary processes. For this purpose, we establish an equivalence between the proximity of the shift operators (which are unit operators) and the associated projector valued...

The aim of this article is the approximation of the principal components analysis (PCA) of a stationary function, defined on , by the PCA of a stationary series. For this, we use a discretization of the real line. We study the behavior of the approximation when the step of discretization decreases.

In this paper, results for the tensor product of discrete and continuous-time processes are presented. They concern the definition and the study of the properties of the processes associated to the (tensor and convolution) products of two (spectral and random) measures. An example for the...