world:markovchains
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world:markovchains [2024/10/17 16:36] alain [Program of the course] |
world:markovchains [2024/12/06 12:57] (current) rdouc |
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| * **Teaching material**: {{world:mainmc-tome1.pdf|pdf version of Markov Chains book}} | * **Teaching material**: {{world:mainmc-tome1.pdf|pdf version of Markov Chains book}} | ||
| - | ^ ^ Prof ^ Chapters ^ Topics ^ Material ^ Cours ^ | + | ^ ^ Prof ^ Chapters ^ Topics ^ Material ^ Cours ^ |
| - | | Sept. 26 | (AD) | Chapt. 1 and 2. | Introduction to Markov chains | {{:world:ex1.pdf| Exercise sheet 1}} | 1 | | + | | Sept. 26 | (AD) | Chapt. 1 and 2. | Introduction to Markov chains | {{:world:ex1.pdf| Exercise sheet 1}} | 1 | |
| - | | Oct. 3 | (AD) | Chapt. 2 and 3 | Invariance, Reversibility. MCMC. Canonical space. | {{:world:ex_2_2024.pdf| Exercise sheet 2}} | 2 | | + | | Oct. 3 | (AD) | Chapt. 2 and 3 | Invariance, Reversibility. MCMC. Canonical space. | {{:world:ex_2_2024.pdf| Exercise sheet 2}} | 2 | |
| - | | Oct. 10 | (AD) | Chapt. 3 | Canonical space (end). Stopping time, (Strong) Markov property, Harmonic functions, martingales | | 3 | | + | | Oct. 17 | | | Pause | | | |
| - | | Oct. 16 | | | Pause | | | | + | | Oct. 24 | (AD) | Chapt. 3 | Canonical space (end). Stopping time, (Strong) Markov property, Harmonic functions, martingales | {{:world:ex_3_2024.pdf| Exercise sheet 3}} | 3 | |
| - | | Oct. 24 | (AD) | Chap 5 | Drift functions. Maximum principle, Solidarity property. Comparison theorem. Atomic chains (atoms, recurrence, transience). | | 4 | | + | | Oct. 31 | (AD) | Chap 5 | Ergodic theory and law of large numbers. | Chapitre 3 de ce {{ :world:polymcmc.pdf |polycopié}} | 4/5 | |
| - | | Oct 31 | (AD) | Chapt 5 | Atomic chains (continued) | | 5 | | + | | Nov 14 | (RD) | Chapt. 6 | Atomic chains. Transience, recurrence. Maximum principle. Uniformly transient sets. | | 6 | |
| - | | Nov 7 | (RD) | Chapt. 8 | Ergodic theory. | Chapitre 3 de ce {{ :world:polymcmc.pdf |polycopié}} | 6 | | + | | Nov 21 | (RD) | Chap 6 | Period, aperiodicity, positive atoms, null-recurrence, Kac's theorem. | | 7 | |
| - | | Nov 14 | (RD) | Chap 9 | Renewal theory, Kac's theorem | | 7 | | + | | Nov 28 | (RD) | Chapt. 6-7-8 | Independent excursions between atoms, coupling inequalities, renewal theory, residual lifetime. | | 8 | |
| - | | Nov 21 | (RD) | Chapt. 9 | Blackwell's and Kendall's theorem | | 9 | | + | | Dec 5 | (RD) | Chapt. 18-19 | Geometric ergodicity. | | 9 | |
| - | | Nov 28 | (RD) | Chapt. 19 | Coupling methods, small sets and geometric ergodicity | {{ :world:polymcmc.pdf |polycopié}} | 10 | | + | | Dec 12 | (RD) | Chap 21 | Central limit theorem. | | 10 | |
| - | | Dec 2 | (RD) | Chap 19 | End of geometric ergodicity. Revision's exercises. | | | | + | |
| + | ====== Lecture notes Session 6-7-8-9 ====== | ||
| + | |||
| + | <WRAP center round tip 60%> | ||
| + | {{ :world:polymarkovchains.pdf |LectureNotes2024}} | ||
| + | </WRAP> | ||
| Line 38: | Line 42: | ||
| * {{ :world:controle.pdf |An examination given in 2019-2020}} | * {{ :world:controle.pdf |An examination given in 2019-2020}} | ||
| * {{ :world:controleCorrige.pdf |Solution of the examination given in 2019-2020}} | * {{ :world:controleCorrige.pdf |Solution of the examination given in 2019-2020}} | ||
| + | |||
| + | ===== Projects ===== | ||
| + | * <fc #ff0000>A short summary (5 pages max) of the paper</fc> is requested before the defense by sending an email to Alain Durmus. You can add technical appendix (with no limitation size). | ||
| + | * The <fc #ff0000>defense will be 20 minutes</fc> long per project + questions. Be as pedagogical as possible, you can highlight a particular proof that interests you if you find it interesting. | ||
| + | * Please read the <color /yellow>{{ :world:guidelinesmda.pdf |guidelines for the report}}</color>. | ||
| + | * If there is any question, please contact Alain Durmus. | ||
| /* ===== Evaluation ===== | /* ===== Evaluation ===== | ||
world/markovchains.1729175794.txt.gz · Last modified: 2024/10/17 16:36 by alain
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