Discrete Probability Models and Methods

Probability on Graphs and Trees, Markov Chains and Random Fields, Entropy and Coding
1. Auflage 2017
ISBN: 978-3-319-43475-9
Verlag: Springer International Publishing

Buch, Englisch, Band 78, 559 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 10855 g

Reihe: Probability Theory and Stochastic Modelling

The emphasis in this book is placed on general models (Markov chains, random fields, random graphs), universal methods (the probabilistic method, the coupling method, the Stein-Chen method, martingale methods, the method of types) and versatile tools (Chernoff's bound, Hoeffding's inequality, Holley's inequality) whose domain of application extends far beyond the present text. Although the examples treated in the book relate to the possible applications, in the communication and computing sciences, in operations research and in physics, this book is in the first instance concerned with theory.

The level of the book is that of a beginning graduate course. It is self-contained, the prerequisites consisting merely of basic calculus (series) and basic linear algebra (matrices). The reader is not assumed to be trained in probability since the first chapters give in considerable detail the background necessary to understand the rest of the book.

Zielgruppe

Graduate

Autoren/Hrsg.

Brémaud, Pierre

Fachgebiete

• Interdisziplinäres Wissenschaften Wissenschaften: Forschung und Information Informationstheorie, Kodierungstheorie
• Mathematik | Informatik Mathematik Operations Research Graphentheorie
• Mathematik | Informatik Mathematik Stochastik Wahrscheinlichkeitsrechnung
• Mathematik | Informatik EDV | Informatik Computerkommunikation & -vernetzung
• Mathematik | Informatik EDV | Informatik Informatik Mathematik für Informatiker
• Mathematik | Informatik EDV | Informatik Daten / Datenbanken Informationstheorie, Kodierungstheorie
• Mathematik | Informatik Mathematik Stochastik Stochastische Prozesse

Inhaltsverzeichnis

Introduction.- 1.Events and probability.- 2.Random variables.- 3.Bounds and inequalities.- 4.Almost-sure convergence.- 5.Coupling and the variation distance.- 6.The probabilistic method.- 7.Codes and trees.- 8.Markov chains.- 9.Branching trees.- 10.Markov fields on graphs.- 11.Random graphs.- 12.Recurrence of Markov chains.- 13.Random walks on graphs.- 14.Asymptotic behaviour of Markov chains.- 15.Monte Carlo sampling.- 16. Convergence rates.- Appendix.- Bibliography.

Über Autor(innen)

Pierre Brémaud obtained his Doctorate in Mathematics from the University of Paris VI and his PhD from the department of Electrical Engineering and Computer Science of the University of California at Berkeley. He is a major contributor to the theory of stochastic processes and their applications, and has authored or co-authored several reference or textbooks on the subject.