Discrete probability models and methods probability on graphs and trees, Markov chains and random fields, entropy and coding /
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 inequali...
| Main Author: | Brémaud, Pierre, |
|---|---|
| Other Authors: | SpringerLink (Online service) |
| Format: | eBook |
| Language: | English |
| Published: |
Cham, Switzerland :
Springer,
2017.
|
| Physical Description: |
1 online resource (xiv, 559 pages) : illustrations. |
| Series: |
Probability theory and stochastic modelling ;
v. 78. |
| Subjects: |
Table of Contents:
- 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.