Discrete Probability Models and Methods

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Sprache: Englisch

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Beschreibung

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.

Über den Autor

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.

Zusammenfassung

Provides a clear overview of the theory

Includes exercises in each chapter

Written by a well known author

Includes supplementary material: [...]

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.

Erscheinungsjahr:	2017
Fachbereich:	Wahrscheinlichkeitstheorie
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Buch
Reihe:	Probability Theory and Stochastic Modelling
Inhalt:	xiv 559 S. 92 s/w Illustr. 559 p. 92 illus.
ISBN-13:	9783319434759
ISBN-10:	3319434756
Sprache:	Englisch
Herstellernummer:	978-3-319-43475-9
Ausstattung / Beilage:	HC runder Rücken kaschiert
Einband:	Gebunden
Autor:	Brémaud, Pierre
Auflage:	1st ed. 2017
Hersteller:	Springer International Publishing Springer International Publishing AG Probability Theory and Stochastic Modelling
Maße:	241 x 160 x 35 mm
Von/Mit:	Pierre Brémaud
Erscheinungsdatum:	03.02.2017
Gewicht:	1,126 kg

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