PROJECT TITLE :

Mathematical Framework for Pseudo-Spectra of Linear Stochastic Difference Equations

ABSTRACT:

Although spectral analysis of stationary stochastic processes has solid mathematical foundations, this is often not continuously thus for a few non-stationary cases. Here, we have a tendency to establish a rigorous mathematical extension of the classic Fourier spectrum to the case in that there are AR roots in the unit circle, i.e., the transfer operate of the linear time-invariant filter has poles on the unit circle. To achieve it we tend to: embed the classical downside in a wider framework, extend the Discrete Time Fourier Rework and defined a replacement Extended Fourier Remodel pair pseudo-covariance operate/pseudo-spectrum. Our approach may be a correct extension of the classical spectral analysis, inside which the Fourier Transform try auto-covariance perform/spectrum may be a particular case. Consequently spectrum and pseudo-spectrum coincide when the primary one is outlined.