Stochastic processes: general definition

Abstract

This short chapter introduces the main topic of this textbook, namely, stochastic processes. As was true for the law of large numbers and the central limit theorem, stochastic processes are collections of random variables defined on the same probability space. These random variables, however, are not usually assumed to be independent. Instead, they are connected by some dependency relationships that can typically be expressed using conditional expectation or probability. In this chapter, we give the general definition of a stochastic process and define martingales and Markov chains along with a couple of examples.