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world:markovchains
Table of Contents
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
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: Markov chains by R. Douc, E. Moulines, P. Priouret and P. Soulier. Springer publishers.
- Teaching material: pdf version of Markov Chains book
| Prof | Chapters | Topics | Material | |
|---|---|---|---|---|
| 24/09 | (AD) | Chapt. 1 and 2. | Conditional distribution, their construction and related operations. Introduction to Markov chains, first definitions | Exercise sheet 1 Lecture notes Notes Monte Carlo |
| 01/10 | (AD) | Chapt. 2 and 3 | Invariant measures / reversibility, Canonical space. | Exercise sheet 2 Exercise sheet 3 Reminders Conditonal expectation Exercises conditional expectation |
| 08/10 | (AD) | Chap 3 | Canonical space (continued). Kolmogorov extension theorem. Strong Markov property. | |
| 15/10 | (AD) | Chapt. 3 | Stopping times, return and hitting times, consequences of Markov property. | |
| 22/10 | No course | |||
| 05/11 | (AD) | Chap 5 | Dynamical systems, Birkhoff theorem, Law of Large Number for Markov chains | |
| 12/11 | (RD) | Chapt. 18 | Uniform and Geometric ergodicity | |
| 19/11 | (RD) | Chapt. 21 | Central limit theorems | |
| 26/11 | (RD) | Chap 22 | Spectral theory | |
| Also courses in December |
Example of an examination
Projects
Contact
| name | email adresses |
|---|---|
| Alain Durmus | alain.durmus “Arobase” polytechnique.edu |
| Randal Douc | randal.douc “Arobase” polytechnique.edu |
world/markovchains.txt · Last modified: 2026/10/01 12:32 by alain
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