Processes with Finite Second Moments. Gaussian Processes

Abstract

The chapter is devoted to the classical “second-order theory” of time-homogeneous processes with finite second moments. Section 22.1 explores the relationships between the covariance function properties and those of the process itself and proves the ergodic theorem (in quadratic mean) for processes with covariance functions vanishing at the infinity. Section 22.2 is devoted to the special case of Gaussian processes, while Sect. 22.3 solves the best linear prediction problem.