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world:markovchains [2025/10/13 21:16] alain [Table] |
world:markovchains [2025/12/16 16:31] (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 ^ | + | ^ ^ Prof ^ Chapters ^ Topics ^ Material ^ |
| - | | 25/09 | (AD) | Chapt. 1 and 2. | Conditional distribution, their construction and related operations. Introduction to Markov chains, first definitions | {{:world:ex1.pdf| Exercise sheet 1}} {{:world:condi_distribu.pdf| Lecture notes}} {{:world:motivations_MC.pdf| Notes Monte Carlo}} | | + | | 25/09 | (AD) | Chapt. 1 and 2. | Conditional distribution, their construction and related operations. Introduction to Markov chains, first definitions | {{:world:ex1.pdf| Exercise sheet 1}} {{:world:condi_distribu.pdf| Lecture notes}} {{:world:motivations_MC.pdf| Notes Monte Carlo}} | |
| - | | 02/10 | (AD) | Chapt. 2 and 3 | Invariant measures / reversibility, Canonical space. | {{:world:ex_2_2025.pdf| Exercise sheet 2}} {{:world:ex_2_2024.pdf| Exercise sheet 3}} {{:world:main_condi_exp_mda.pdf| Reminders Conditonal expectation}} {{:world:main_exos_condi_mda.pdf| Exercises conditional expectation}} | | + | | 02/10 | (AD) | Chapt. 2 and 3 | Invariant measures / reversibility, Canonical space. | {{:world:ex_2_2025.pdf| Exercise sheet 2}} {{:world:ex_2_2024.pdf| Exercise sheet 3}} {{:world:main_condi_exp_mda.pdf| Reminders Conditonal expectation}} {{:world:main_exos_condi_mda.pdf| Exercises conditional expectation}} | |
| - | | 09/10 | (AD) | Chap 3 | Canonical space (continued). Kolmogorov extension theorem. Strong Markov property. | {{:world:ex_4_2025.pdf| Exercise sheet 4}} | | + | | 09/10 | (AD) | Chap 3 | Canonical space (continued). Kolmogorov extension theorem. Strong Markov property. | {{:world:ex_4_2025.pdf| Exercise sheet 4}} | |
| - | | 16/10 | (AD) | Chapt. 3 | Dynamical systems, Birkhoff theorem, Metrics: TV norms, V norms, Wasserstein. | | | + | | 16/10 | (AD) | Chapt. 3 | Stopping times, return and hitting times, consequences of Markov property. | {{:world:ex_5_2025.pdf| Exercise sheet 5}} | |
| - | | 23/10 or 30/10 | (RD) | Chap 5 | Geometric ergodicity. | | | + | | 23/10 | (AD) | Chap 5 | Dynamical systems, Birkhoff theorem, Law of Large Number for Markov chains | | |
| - | | 06/11 | (RD) | Chapt. 6 | Central Limit Theorems | | | + | | 06/11 | (RD) | No course | Opening date for Projects | | |
| - | | 13/11 | (RD) | Chap 6 | Rosenthal inequalities (Alain). | | | + | | 13/11 | (RD) | No course | Closing date for Projects | | |
| - | | 20/11 | (AD) | Chapt. 6-7-8 | Quantitative Central Limit theorems | | | + | | 20/11 | (RD) | Chapt. 18 | Uniform and Geometric ergodicity | {{ :world:geom-erg-clt-spectral.pdf | The last 3 courses concerns 3 chapters on geometric ergodicity, CLT and spectral theory}} | |
| - | | 27/11 | (RD) | Chapt. 18-19 | Convergence via spectral methods | | | + | | 27/11 | (RD) | Chapt. 21 | Central limit theorems | ::: | |
| - | | 04/12 | (AD) | Chap 21 | Contractive convergence via curvature lower bounds. | | | + | | 11/12 | (RD) | Chap 22 | Spectral theory | ::: | |
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| ===== Projects ===== | ===== 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). | + | <color /yellow>[[world:projet-mda-2025|Please click here for the projects]]</color> |
| - | * 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.1760383001.txt.gz · Last modified: 2025/10/13 21:16 by alain
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