{{tag>:markov_chains}}
====== 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 ======
* [[https://docs.google.com/forms/d/e/1FAIpQLSdjk1HhX6lfoIpbrT7aWqFPoZcpwtp4aSwMxw2PxM55MgVtnA/viewform?usp=sf_link|Please register here]]
====== 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: [[https://www.springer.com/gp/book/9783319977034|Markov chains]] by R. Douc, E. Moulines, P. Priouret and P. Soulier. Springer publishers.
* **Teaching material**: {{world:mainmc-tome1.pdf|pdf version of Markov Chains book}}
^ ^ Prof ^ Chapters ^ Topics ^ Material ^
| 25/09 | (AD) | Chapt. 1 and 2. | Conditional distribution, their construction and related operations. Introduction to Markov chains, first definitions | {{:world:ex1.pdf| Exercise sheet 1}} {{:world:condi_distribu.pdf| Lecture notes}} {{:world:motivations_MC.pdf| Notes Monte Carlo}} |
| 02/10 | (AD) | Chapt. 2 and 3 | Invariant measures / reversibility, Canonical space. | {{:world:ex_2_2025.pdf| Exercise sheet 2}} {{:world:ex_2_2024.pdf| Exercise sheet 3}} {{:world:main_condi_exp_mda.pdf| Reminders Conditonal expectation}} {{:world:main_exos_condi_mda.pdf| Exercises conditional expectation}} |
| 09/10 | (AD) | Chap 3 | Canonical space (continued). Kolmogorov extension theorem. Strong Markov property. | {{:world:ex_4_2025.pdf| Exercise sheet 4}} |
| 16/10 | (AD) | Chapt. 3 | Dynamical systems, Birkhoff theorem, Metrics: TV norms, V norms, Wasserstein. | |
| 23/10 or 30/10 | (RD) | Chap 5 | Geometric ergodicity. | |
| 06/11 | (RD) | Chapt. 6 | Central Limit Theorems | |
| 13/11 | (RD) | Chap 6 | Rosenthal inequalities (Alain). | |
| 20/11 | (AD) | Chapt. 6-7-8 | Quantitative Central Limit theorems | |
| 27/11 | (RD) | Chapt. 18-19 | Convergence via spectral methods | |
| 04/12 | (AD) | Chap 21 | Contractive convergence via curvature lower bounds. | |
====== Lecture notes Session 6-7-8-9 ======
{{ :world:polymarkovchains.pdf |LectureNotes2024}}
===== Example of an examination =====
* {{ :world:controle.pdf |An examination given in 2019-2020}}
* {{ :world:controleCorrige.pdf |Solution of the examination given in 2019-2020}}
===== 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 {{ :world:guidelinesmda.pdf |guidelines for the report}}.
* If there is any question, please contact Alain Durmus.
/* ===== Evaluation =====
**Evaluation**: The exam will take place on Thursday, December 16, 2021. It is a 3-hour table-top assignment [all documents are allowed].
*/
===== Contact =====
^ name ^ email adresses ^
| Alain Durmus | alain.durmus **"Arobase"** polytechnique.edu |
| Randal Douc | randal.douc **"Arobase"** polytechnique.edu |
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~~DISCUSSION~~