Probability Theory and Stochastic Processes

The ultimate objective of this book is to present a panoramic view of the main stochastic processes with an impact on applications including complete proofs and exercises. Random processes play a central role in the applied sciences such as operations research, insurance, finance, biology, physics, computer and communications networks and signal processing, among others. In order to help the reader to reach the level of technical autonomy sufficient to understand the presented models, this book includes a reasonable dose of probability theory. On the other hand, the study of stochastic processes gives an opportunity to apply the main theoretical results of probability theory beyond classroom examples and in a non-trivial manner that makes this discipline look more attractive for the applications oriented student. One can distinguish three parts in this book. The first four chapters are about probability theory, Chapters 5 to 8 about random sequences, or discrete-time stochastic processes, and the rest of the book about stochastic processes and point processes. There is sufficient modularity for the instructor or the self-teaching reader to design a course or a study program adapted to her/his specific needs. This book is in a large measure self-contained.