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world:markovchains
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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
Student Projects on Markov chains
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 | 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 8 | Renewal theory, Blackwell's and Kendall's theorems. Geometric ergodicity by the renewal approach. | 5 | |
| Nov 9 | (RD) | Chapt. 9 | small sets, irreducibility, aperiodicity, | 6 | |
| Nov 16 | (RD) | Chap 11, 18 | irreducibility (end…), Splitting, existence of an invariant measure. | Tutorial 7 | 7 |
| Nov 23 | (RD) | Chapt. 5 | Ergod. Theorem. Notes de cours | Chapitre 3 de ce polycopié | 8 |
| Nov 30 | (RD) | Chapt. 18 | Geometric ergodicity by Hairer's method La preuve d'Hairer se trouve ici | Notes de cours | 9 |
| Dec 7 | (RD) | Chapt. 19 | Coupling methods and geometric ergodicity | 10 |
Example of an examination
Contact
| name | email adresses |
|---|---|
| Alain Durmus | alain.durmus “Arobase” polytechnique.edu |
| Randal Douc | randal.douc “Arobase” polytechnique.edu |
world/markovchains.txt · Last modified: 2023/12/03 22:13 by rdouc
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