{{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                                                                                                                                                                                                                         ^
| 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         | Stopping times, return and hitting times, consequences of Markov property.                                             | {{:world:ex_5_2025.pdf| Exercise sheet 5}}                                                                                                                                                                                       |
| 23/10  | (AD)  | Chap 5           | Dynamical systems, Birkhoff theorem, Law of Large Number for Markov chains                                             |                                                                                                                                                                                                                                  |
| 06/11  | (RD)  | No course        | Opening date for Projects                                                                                              |                                                                                                                                                                                                                                  |
| 13/11  | (RD)  | No course        | Closing date for Projects                                                                                              |                                                                                                                                                                                                                                  |
| 20/11  | (RD)  | Chapt. 18        | Uniform and Geometric ergodicity                                                                                       |  {{ :world:geom-erg-clt-spectral.pdf | The last 3 courses concerns 3 chapters on geometric ergodicity, CLT and spectral theory}}                                                                                                                                                                           |
| 27/11  | (RD)  | Chapt. 21        | Central limit theorems                                                                                                 | :::                                                                                                                                                                                                                              |
| 11/12  | (RD)  | Chap 22          | Spectral theory                                                                                                        |  :::                                                                                                                                                                                                                             |



====== 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 =====
<color /yellow>[[world:projet-mda-2025|Please click here for the projects]]</color>

/* ===== 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  |


----

~~DISCUSSION~~