Discrete Probability Models and Methods : Probability on Graphs and Trees, Markov Chains and Random Fields, Entropy and Coding. 1st ed. 2017

種類:

電子ブック

責任表示:

by Pierre Brémaud

出版情報:

Cham : Springer International Publishing : Imprint: Springer, 2017

著者名:

• Brémaud, Pierre.
• SpringerLink (Online service)

シリーズ名:

Probability Theory and Stochastic Modelling ; 78

ISBN:

9783319434766 [3319434764]    

注記:

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.
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. .

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