Spectral Theory

Abstract

The spectral theory of point processes and random measures is concerned with frequency (i.e., Fourier) representations of various kinds and degrees of generality. In this chapter we look first at the frequency representation of the reduced second-order measures introduced in Chapter 10 and then at frequency representations and related questions for the process itself. Such representations have less value in the present context than in the continuous (especially, Gaussian) context, for reasons already touched on in previous chapters: the mean square representations rarely preserve the character of the original trajectories of the process, and the linear predictors to which they give rise can often be improved upon by quite simple nonlinear predictors (cf Chapter 13).