A Course in Statistics with R

Chapter 10Stochastic Processes

Package(s): sna

Dataset(s): testtpm, testtpm2, testtpm3

10.1 Introduction

Stochastic processes commonly refer to a collection of random variables. Such a collection may vary over time, sample number, geographical location, etc. It is to be noted that a stochastic process may consist of finite, countably infinite, or uncountably infinite collections of random variables. An important characteristic of the stochastic process is that it allows us to relax the assumption of independence for a sequence of random variables.

Definition 10.1.1

A Stochastic Process is a collection of random variables

10.1

where may be a finite set, or countable set, or an interval.

A few examples are in order.

Example 10.1.1. Examples of Stochastic Processes

We will consider situations where a stochastic process may be discrete or continuous.

• The maximum temperature of the day. Let denote the maximum temperature recorded on the day. Then, the collection forms an example ...