Introduction to Stochastic Processes and Simulation

1Basic Reminders of Probability

CONCEPTS DISCUSSED IN THIS CHAPTER.– The concept of probability is at the heart of this book. It is therefore necessary to master the corresponding concepts. In principle, the reader should already have the required knowledge. However, experience shows that a reminder is always necessary to refresh knowledge which may have been learnt a while ago.

In this chapter, we will discuss the nature of chance and an empirical approach to probability, based on counting possible results from experience.

We will move on to a formal approach to probability, based on the set theory, which applies to previous experimental cases, and then a statistical definition of probability with the law of large numbers.

If the reader is proficient in these concepts, they can skip the corresponding sections.

Finally, we will end with the very important concept of composite probability, which is illustrated by a figure showing states of a system, transitions between states and graphs representative of the possible evolution of a system.

Recommended reading: [BRE 09, DEH 82, DOD 08, ENG 76, ROS 93, SAP 11].

1.1. Chance

The Larousse dictionary gives two meanings for the word “chance”:

• – “power regarded as the cause of apparently incidental or inexplicable events”;
• – “unforeseen or unforeseeable circumstances, the effects of which may be favorable or unfavorable to someone”.

The first definition is actually a double one:

• – it introduces the concept of causality according ...