Chapter 4 - Stochastic Processes

Abstract

This chapter presents an overview of stochastic processes. A family of random variables {X(t), t ∈ T} is called a stochastic process. Thus, for each t ∈ T, where T is the index set of the process, X(t) is a random variable. An element of T is usually referred to as a time parameter and t is often referred to as time, although this is not a part of the definition. The state space of the process is the set of all possible values that the random variables X(t) can assume. Each of these values is called a state of the process. Stochastic processes are classified in a number of ways, such as by the index set and by the state space. If T = {0, 1, 2,….} or T = {0, ± 1, ±2,….}, then the stochastic process is said to be a discrete parameter process.