Introduction to Stochastic Processes and Simulation

Gerard-Michel Cochard

• Publisher: Wiley-ISTE
• Year: 2019
• ISBN:
  9781119670780
• Edition: 1
• Topic: Computer Science
• Subtopic: Information Technology
• Index: Computer Science

Mastering chance has, for a long time, been a preoccupation of mathematical research. Today, we possess a predictive approach to the evolution of systems based on the theory of probabilities. Even so, uncovering this subject is sometimes complex, because it necessitates a good knowledge of the underlying mathematics. This book offers an introduction to the processes linked to the fluctuations in chance and the use of numerical methods to approach solutions that are difficult to obtain through an analytical approach. It takes classic examples of inventory and queueing management, and addresses more diverse subjects such as equipment reliability, genetics, population dynamics, physics and even market finance. It is addressed to those at Masters level, at university, engineering school or management school, but also to an audience of those in continuing education, in order that they may discover the vast field of decision support.

Part 1
Basic Mathematical Concepts

1
Basic 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 to which an inexplicable event would nevertheless be due to an unknown cause; knowing the cause and the mechanisms that result from it, one could (theoretically) explain the inexplicable. Thus, if a passerby is hit on the head by a flowerpot that has fallen from a window after a gust of wind, it is...

Table of contents

• Cover
• Table of Contents
• Preface
• Part 1: Basic Mathematical Concepts
• Part 2: Stochastic Processes
• Part 3: Simulation
• References
• Index
• End User License Agreement