{{tag>:markov_chains}}

====== A course on Markov Chains: Advanced topics ======
  * **Trick:** The real address of this page is: <color /yellow>https://wiki.randaldouc.xyz/doku.php?id=world:markovchains</color> but there is also an equivalent (more simple) address: https://lstu.fr/markovchains

====== Registration to the course ======
 
  * <color /yellow> [[https://docs.google.com/forms/d/e/1FAIpQLSdjk1HhX6lfoIpbrT7aWqFPoZcpwtp4aSwMxw2PxM55MgVtnA/viewform?usp=sf_link|Please register here]] </color>


====== Program of the course ======
  * **Where?** Institut de Mathématiques d'ORSAY. Room: 1A14. 
  * **When?** Every course will hold on Thursday <color red>from 9H to 12H00</color> (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                                                                   ^ Cours  ^
| Sept. 26  | (AD)  | Chapt. 1 and 2.  | Introduction to Markov chains                                                                    | {{:world:ex1.pdf| Exercise sheet 1}}                                       | 1      |
| Oct. 3    | (AD)  | Chapt. 2 and 3   | Invariance, Reversibility. MCMC. Canonical space.                                                |  {{:world:ex_2_2024.pdf| Exercise sheet 2}}                                | 2      |
| Oct. 17   |       |                  | Pause                                                                                            |                                                                            |        |
| Oct. 24   | (AD)  | Chapt. 3         | Canonical space (end). Stopping time, (Strong) Markov property, Harmonic functions, martingales  | {{:world:ex_3_2024.pdf| Exercise sheet 3}}                                 | 3      |
| Oct. 31   | (AD)  | Chap 5           | Ergodic theory and law of large numbers.                                                         | Chapitre 3 de ce {{ :world:polymcmc.pdf |polycopié}}                       | 4/5    |
| Nov 14    | (RD)  | Chapt. 6         | Atomic chains. Transience, recurrence. Maximum principle. Uniformly transient sets.              |  | 6      |
| Nov 21    | (RD)  | Chap  6          | Period, aperiodicity, positive atoms, null-recurrence, Kac's theorem.                            |                                                                            | 7      |
| Nov 28    | (RD)  | Chapt. 6-7-8     | Independent excursions between atoms, coupling inequalities, renewal theory, residual lifetime.  |                                                                            | 8      |
| Dec 5     | (RD)  | Chapt. 18-19     | Geometric ergodicity.                                                                            |                                                                            | 9      |
| Dec 12    | (RD)  | Chap 21          | Central limit theorem.                                                                           |                                                                            | 10     |


====== Lecture notes Session 6-7-8-9 ======

<WRAP center round tip 60%>
 {{ :world:polymarkovchains.pdf |LectureNotes2024}}
</WRAP>


===== 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 =====
  * <fc #ff0000>A short summary (5 pages max) of the paper</fc> is requested before the defense by sending an email to Alain Durmus. You can add technical appendix (with no limitation size).
  * The <fc #ff0000>defense will be 20 minutes</fc> 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 <color /yellow>{{ :world:guidelinesmda.pdf |guidelines for the report}}</color>.    
  * 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~~