Gaussian Variables and Gaussian Processes

Abstract

Gaussian random processes play an important role both in theoretical probability and in various applied models. We start by recalling basic facts about Gaussian random variables and Gaussian vectors. We then discuss Gaussian spaces and Gaussian processes, and we establish the fundamental properties concerning independence and conditioning in the Gaussian setting. We finally introduce the notion of a Gaussian white noise, which is used to give a simple construction of Brownian motion in the next chapter.