Probability theory and stochastic processes / Pierre Brémaud.
- Cham, Switzerland : Springer, 
xvii, 713 pages ; 24 cm.
- The ultimate objective of this book is to present a panoramic view of the main stochastic processes which have an impact on applications, with complete proofs and exercises. Random processes play a central role in the applied sciences, including operations research, insurance, finance, biology, physics, computer and communications networks, and signal processing. In order to help the reader to reach a 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 to the applications-oriented student. One can distinguish three parts of this book. The first four chapters are about probability theory, Chapters 5 to 8 concern random sequences, or discrete-time stochastic processes, and the rest of the book focuses on 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.
- Introduction.-Warming Up
Integration Theory for Probability
Probability and Expectation
Convergence of random sequences
Generalities on Stochastic Processes
Continuous-Time Markov Chains
Renewal Theory in Continuous Time
Wide-sense Stationary Stochastic Processes
An Introduction to Itô's Calculus
Appenndix: Number Theory and Linear Algebra
Proof of Paul Lévy's Criterion
Direct Riemann Integrability
- Includes bibliographical references and index.
- Other format:
- Electronic version: Brémaud, Pierre. Probability theory and stochastic processes.
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