Introduction to Stochastic Processes and Simulation

9Principles of Simulation

CONCEPTS DISCUSSED IN THIS CHAPTER.– In this chapter, we are interested in simulation in general. We will take characteristic examples to illustrate the concept.

We will begin by defining the word “simulation”, mainly in relation to the content of this book.

Then, we will focus on stochastic simulation, which involves chance. Chance comes in the form of using random numbers. Nowadays, the computer is a valuable tool for performing simulations and generating random numbers.

To make numerical simulations on a computer, it is necessary to produce data that represent samples for the phenomena studied.

A modeling of manipulated random variables involves the normal probability distributions in general, although there is nothing to stop us defining our own probability laws from statistical observations. In the case of the normal distribution, we will show how a simulation constrained by these laws is carried out.

Recommended reading: [BAR 01, BER 07, DOD 08, FAU 14, VAL 07].

9.1. General information on simulation

What does the word “simulation” mean? To find out, we examine, like everyone else, the dictionary definitions. And here we have a fairly large choice.

Larousse’s definition of the word “simulation”¹:

“Voluntary or semi-voluntary imitation of a mental or physical disorder.

Representation of the behavior of a physical, industrial, biological, economic or military process by means of a material model whose parameters and variables are the images of ...