Welcome to Randal Douc's wiki

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====== 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>
====== 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}}
 
^ Date      ^ Prof  ^ Chapters         ^ Topics                                                                                                                                                                          ^ Material                                                  ^ Cours  ^
| Sept. 21  | (AD)  | Chapt. 1 and 2.  | Introduction to Markov chains, invariant measure, reversibility. MCMC.                                                                                                          |              | 1      |
| Sept. 28  | (AD)  | Chapt. 3 and 4   | Stopping time, canonical space, (Strong) Markov property, Kac formula for invariant probability measures, Harmonic functions, martingales, drift functions. Maximum principle.  |                 | 2      |
| Oct. 5    | (AD)  | Chapt. 4 and 6   | Solidarity property, comparison theorem, Atomic chains (atoms, 							recurrence, transience)                                                                                   |                         | 3      |
| Oct. 12   | (AD)  | Chapt  6,7       | End of Atomic chains. Coupling results on discrete Markov chains.                                                                                                               |                                                           | 4      |
| Oct 26    | (AD)  | Chapt  8         | Renewal theory, Blackwell's and Kendall's theorems. Geometric ergodicity by the renewal approach.                                                                               |                                                           | 5      |
| Nov 2     | (RD)  | Chapt. 9         | small sets, irreducibility, aperiodicity,                                                                                                                                       |                                                           | 6      |
| Nov 9     | (RD)  | Chap  11,  18    | irreducibility (end...), Splitting, existence of an invariant measure. <color /yellow> </color>                                                                                 | {{world:exo-semaine7.pdf|Tutorial 7}}                     | 7      |
| Nov 16    | (RD)  | Chapt. 5         | Ergod. Theorem.  {{ :world:mc.pdf |Notes de cours}}                                                                                                                             | Chapitre 3 de ce {{ :world:polymcmcm2ds.pdf |polycopié}}  | 8      |
| Nov 23    | (RD)  | Chapt. 18        | Geometric ergodicity by Hairer's method [[http://www.hairer.org/papers/harris.pdf|La preuve d'Hairer se trouve ici]]                                                            | {{world:cours8.pdf| Notes de cours}}                      | 9      |
| Nov 30    | (RD)  | Chapt. 19        | Coupling methods and geometric ergodicity                                                                                                                                       |                                                           | 10     |

===== Example of an examination =====
{{ :world:controle.pdf |An 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 =====

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