Multipoint Schur algorithm, II: generalized moment problems, Gaussian processes and prediction

TL;DR

This paper introduces a new class of Gaussian processes based on generalized moment problems, providing spectral representations and solutions to prediction problems, with examples involving orthogonal rational functions.

Contribution

It applies classical generalized moment problem theory to define and analyze a novel class of Gaussian processes with spectral and prediction properties.

Findings

Defined a special class of Gaussian processes using moment problem theory

Derived spectral representations for these processes

Solved the prediction problem for the class

Abstract

We use nowdays classical theory of generalized moment problems by Krein-Nudelman [1977] to define a special class of stochastic Gaussian processes. The class contains, of course, stationary Gaussian processes. We obtain a spectral representation for the processes from this class and we solve the corresponding prediction problem. The orthogonal rational functions on the unit circle lead to a class of Gaussian processes providing an example for the above construction.