world:markovchains
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world:markovchains [2023/09/15 19:09] 93.19.156.200 [Table] |
world:markovchains [2024/01/09 13:29] (current) rdouc |
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| - | {{page>:defs}} | ||
| {{tag>:markov_chains}} | {{tag>:markov_chains}} | ||
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| * <color /yellow> [[https://docs.google.com/forms/d/e/1FAIpQLSesxddvgaTVJTScg66qSrOlW3gT1hhL4A8Jslae5jXEDShV7Q/viewform|Please register here]] </color> | * <color /yellow> [[https://docs.google.com/forms/d/e/1FAIpQLSesxddvgaTVJTScg66qSrOlW3gT1hhL4A8Jslae5jXEDShV7Q/viewform|Please register here]] </color> | ||
| + | |||
| + | ====== Student Projects on Markov chains ====== | ||
| + | * <color /yellow>[[world:projet-mda-2024| Click here to jump and register to the Project page]] </color> | ||
| + | |||
| ====== Program of the course ====== | ====== Program of the course ====== | ||
| * **Where?** Institut de Mathématiques d'ORSAY. Room: 1A14. | * **Where?** Institut de Mathématiques d'ORSAY. Room: 1A14. | ||
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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}} | ||
| - | ^ Date ^ Prof ^ Chapters ^ Topics ^ Material ^ Cours ^ | + | ^ ^ Prof ^ Chapters ^ Topics ^ Material ^ Cours ^ |
| - | | Sept. 21 | (AD) | Chapt. 1 and 2. | Introduction to Markov chains, invariant measure, reversibility. MCMC. | {{ :world:cours1.pdf | Notes de cours 1}} | 1 | | + | | Sept. 21 | (AD) | Chapt. 1 and 2. | Introduction to Markov chains, invariant measure, | | 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. | {{world:exo-2020-semaine2.pdf|Tutorial 2}} | 2 | | + | | Sept. 28 | (AD) | Chapt. 2 and 3 | Reversibility. MCMC. Canonical space. Stopping time, (Strong) Markov property | | 2 | |
| - | | Oct. 5 | (AD) | Chapt. 4 and 6 | Solidarity property, comparison theorem, Atomic chains (atoms, recurrence, transience) | {{world:tutorial3.pdf|Tutorial 3}} | 3 | | + | | Oct. 5 | (AD) | Chapt. 3 | Harmonic functions, martingales, drift functions. Maximum principle, Solidarity property. Comparison theorem. | | 3 | |
| - | | Oct. 12 | (AD) | Chapt 6,7 | End of Atomic chains. Coupling results on discrete Markov chains. | | 4 | | + | | Oct. 12 | (AD) | Chapt 6,7 | Atomic chains (atoms, recurrence, transience). | | 4 | |
| - | | Oct 26 | (AD) | Chapt 8 | Renewal theory, Blackwell's and Kendall's theorems. Geometric ergodicity by the renewal approach. | | 5 | | + | | Oct 19 | (AD) | Chapt 5 | Atomic chains (continued) | | 5 | |
| - | | Nov 2 | (RD) | Chapt. 9 | small sets, irreducibility, aperiodicity, | | 6 | | + | | Nov 9 | (RD) | Chapt. 8 | Ergodic theory. | Chapitre 3 de ce {{ :world:polymcmc.pdf |polycopié}} | 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) | Chap 9 | Renewal theory, Kac's theorem | | 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) | Postponed | | | 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. 9 | Blackwell's and Kendall's theorem | | 9 | |
| - | | Nov 30 | (RD) | Chapt. 19 | Coupling methods and geometric ergodicity | | 10 | | + | | Dec 7 | (RD) | Chapt. 19 | Coupling methods, small sets and geometric ergodicity | {{ :world:polymcmc.pdf |polycopié}} | 10 | |
| + | | Dec 14 | (RD) | Chap 19 | End of geometric ergodicity. Revision's exercises. | | | | ||
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| ===== Example of an examination ===== | ===== Example of an examination ===== | ||
| - | {{ :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}} | ||
| /* ===== Evaluation ===== | /* ===== Evaluation ===== | ||
world/markovchains.1694797796.txt.gz · Last modified: 2023/09/15 19:09 by 93.19.156.200
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