{{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/1FAIpQLSesxddvgaTVJTScg66qSrOlW3gT1hhL4A8Jslae5jXEDShV7Q/viewform|Please register here]] </color>

====== Student Projects on Markov chains ======
  * <color /yellow>[[world:projet-mda-2024| Click here to jump and register to the Project page]] </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. 21  | (AD)  | Chapt. 1 and 2.  | Introduction to Markov chains, invariant measure,                                                              |                                                       | 1      |
| Sept. 28  | (AD)  | Chapt. 2 and 3   | Reversibility. MCMC. Canonical space. Stopping time, (Strong) Markov property                                  |                                                       | 2      |
| Oct. 5    | (AD)  | Chapt. 3         | Harmonic functions, martingales, drift functions. Maximum principle, Solidarity property. Comparison theorem.  |                                                       | 3      |
| Oct. 12   | (AD)  | Chapt  6,7       | Atomic chains (atoms, recurrence, transience).                                                                 |                                                       | 4      |
| Oct 19    | (AD)  | Chapt  5         | Atomic chains (continued)                                                                                      |                                                       | 5      |
| Nov 9     | (RD)  | Chapt. 8         | Ergodic theory.                                                                                                | Chapitre 3 de ce {{ :world:polymcmc.pdf |polycopié}}  | 6      |
| Nov 16    | (RD)  | Chap  9          | Renewal theory, Kac's theorem                                                                                  |                                                       | 7      |
| Nov 23    | (RD)  | Postponed        |                                                                                                                |                                                       | 8      |
| Nov 30    | (RD)  | Chapt. 9         | Blackwell's and Kendall's theorem                                                                              |                                                       | 9      |
| Dec 7     | (RD)  | Chapt. 19        | Coupling methods, small sets and geometric ergodicity                                                          | {{ :world:polymcmc.pdf |polycopié}}                   | 10     |
| Dec 14    | (RD)  | Chap 19          | End of geometric ergodicity. Revision's exercises.                                                             |                                                       |        |




===== Example of an examination =====
  * {{ :world:controle.pdf |An examination given in 2019-2020}}
  * {{ :world:controleCorrige.pdf |Solution of the examination given in 2019-2020}}

/* ===== 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~~