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world:markovchains
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Table of Contents
A course on Markov Chains: Advanced topics
- Trick: The real address of this page is: https://wiki.randaldouc.xyz/doku.php?id=world:markovchains but there is also an equivalent (more simple) address: https://lstu.fr/markovchains
Registration to the course
Program of the course
- Where? Institut de Mathématiques d'ORSAY. Room: 1A14.
- When? Every course will hold on Thursday from 9H to 12H00 (exact dates are given below).
- Who? The list of the teachers are given below with their acronyms:
- AD: Alain Durmus.
- RD: Randal Douc.
- What? The chapters refer to the book: Markov chains by R. Douc, E. Moulines, P. Priouret and P. Soulier. Springer publishers.
- Teaching material: pdf version of Markov Chains book
| Prof | Chapters | Topics | Material | Cours | |
|---|---|---|---|---|---|
| Sept. 26 | (AD) | Chapt. 1 and 2. | Introduction to Markov chains | Exercise sheet 1 | 1 |
| Oct. 3 | (AD) | Chapt. 2 and 3 | Invariance, Reversibility. MCMC. Canonical space. | Exercise sheet 2 | 2 |
| Oct. 10 | (AD) | Chapt. 3 | Canonical space (end). Stopping time, (Strong) Markov property, Harmonic functions, martingales | 3 | |
| Oct. 16 | Pause | ||||
| Oct. 24 | (AD) | Chap 5 | Drift functions. Maximum principle, Solidarity property. Comparison theorem. Atomic chains (atoms, recurrence, transience). | 4 | |
| Oct 31 | (AD) | Chapt 5 | Atomic chains (continued) | 5 | |
| Nov 7 | (RD) | Chapt. 8 | Ergodic theory. | Chapitre 3 de ce polycopié | 6 |
| Nov 14 | (RD) | Chap 9 | Renewal theory, Kac's theorem | 7 | |
| Nov 21 | (RD) | Chapt. 9 | Blackwell's and Kendall's theorem | 9 | |
| Nov 28 | (RD) | Chapt. 19 | Coupling methods, small sets and geometric ergodicity | polycopié | 10 |
| Dec 2 | (RD) | Chap 19 | End of geometric ergodicity. Revision's exercises. |
Example of an examination
Contact
| name | email adresses |
|---|---|
| Alain Durmus | alain.durmus “Arobase” polytechnique.edu |
| Randal Douc | randal.douc “Arobase” polytechnique.edu |
world/markovchains.1729175794.txt.gz · Last modified: 2024/10/17 16:36 by alain
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