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商品コード: 9783319434759

Discrete Probability - Models and Methods

販売価格(税込): 11,777 円  (本体価格: 10,905 円+税)
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分野別 > 数学 > 統計学・確率論

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書名

Discrete Probability - Models and Methods: Probability on Graphs and Trees, Markov Chains and Random Fields, Entropy and Coding
著者・編者 Bremaud, P.
出版社/発行元 Springer
発行年/月 2017年1月   
装丁 Hardcover
ページ数/巻数 630 ページ
ISBN 978-3-319-43475-9
発送予定 海外倉庫よりお取り寄せ 2-3週間以内に発送します

 

Desciption

 

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.

 

Contents:

 

1 Events and Probability
2 Random Variables
3 Bounds and Inequalities
4 Almost Sure Convergence
5 The probabilistic Method
6 Markov Chain Models
7 Recurrence of Markov Chains
8 Random Walks on Graphs
9 Markov Fields on Graphs
10 Random Graphs
11 Coding Trees
12 Shannon’s Capacity Theorem
13 The Method of Types
14 Universal Source Coding
15 Asymptotic Behaviour of Markov Chains
16 The Coupling Method
17 Martingale Methods
18 Discrete Renewal Theory
19 Monte Carlo
21 Exact Sampling

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