Basics of Stochastic Processes, Point and Marked Point Processes

Abstract

The study of the dynamic performance of engineered systems subject to uncertainty requires the use of tools from stochastic processes. Although stochastic processes have been used extensively in many disciplines (e.g., see [1–4]), this chapter will focus on the the mathematical background that supports the models presented later in the book. The topics of stochastic processes presented in this chapter include definition of point processes, basic theorems, renewal theory, and regenerative processes. Not all theory about stochastic processes presented in this book is included in this chapter; some additional concepts and formalisms are presented and discussed in the following chapters when appropriate. This chapter is not intended as a comprehensive review, and several references are included for the reader to explore some of the topics in more detail.