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world:markovchains
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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 | |
|---|---|---|---|---|---|
| 1 | (AD) | Chapt. 1 and 2. | Introduction to Markov chains, first definitions, Markov kernel, Elementary operations. Invariant measures / reversibility | Exercise sheet 1 | 1 |
| 2 | (AD) | Chapt. 2 and 3 | Canonical space. Kolmogorov extension theorem. Strong Markov property.Applications of the Markov properties: Stopping times. | Exercise sheet 2 | 2 |
| 3 | (AD) | Dynamical systems, Birkhoff theorem | |||
| 4 | (AD) | Chapt. 3 | Metrics: TV norms, V norms, Wasserstein. | Exercise sheet 3 | 3 |
| Oct. 31 | (RD) | Chap 5 | Geometric ergodicity. | Chapitre 3 de ce polycopié | 4/5 |
| Nov 14 | (RD) | Chapt. 6 | Central Limit Theorems | 6 | |
| Nov 21 | (RD) | Chap 6 | Rosenthal inequalities (Alain). | 7 | |
| Nov 28 | (AD) | Chapt. 6-7-8 | Quantitative Central Limit theorems | 8 | |
| Dec 5 | (RD) | Chapt. 18-19 | Convergence via spectral methods | 9 | |
| Dec 12 | (AD) | Chap 21 | Contractive convergence via curvature lower bounds. | 10 |
Lecture notes Session 6-7-8-9
Example of an examination
Projects
- A short summary (5 pages max) of the paper is requested before the defense by sending an email to Alain Durmus. You can add technical appendix (with no limitation size).
- The defense will be 20 minutes long per project + questions. Be as pedagogical as possible, you can highlight a particular proof that interests you if you find it interesting.
- Please read the guidelines for the report.
- If there is any question, please contact Alain Durmus.
Contact
| name | email adresses |
|---|---|
| Alain Durmus | alain.durmus “Arobase” polytechnique.edu |
| Randal Douc | randal.douc “Arobase” polytechnique.edu |
world/markovchains.txt · Last modified: 2025/09/12 15:58 by rdouc
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