Stochastic Processes: Basic Concepts and Definitions

Abstract

In this chapter and the next, we state a number of important results which are necessary for the work of the later chapters. Some of them might not be explicitly referred to in the later work, but they all form essential links in the chain of reasoning. To present the proofs of all of these results here would require preparatory background material which would considerably increase both the size and scope of this book. We therefore adopt the following approach with the aim of making the development of the text as self-contained as possible. We omit the proofs of those theorems which are treated in detail in well-known standard textbooks, such as P. A. Meyer’s book, Probability and Potentials [41]. However, those proofs will be presented which are not available in existing books and are to be found scattered in the literature, or which discuss ideas specially relevant to our purpose.