world:markovchains
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world:markovchains [2024/12/06 12:56] rdouc |
world:markovchains [2025/10/03 14:38] (current) alain [Table] |
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| ====== Program of the course ====== | ====== Program of the course ====== | ||
| - | * **Where?** Institut de Mathématiques d'ORSAY. Room: 1A14. | + | * **Where?** Institut de Mathématiques d'ORSAY. Room: 1A14. |
| - | * **When?** Every course will hold on Thursday <color red>from 9H to 12H00</color> (exact dates are given below). | + | * **When?** Every course will hold on Thursday <color red>from 9H to 12H00</color> (exact dates are given below). |
| - | * **Who?** The list of the teachers are given below with their acronyms: | + | * **Who?** The list of the teachers are given below with their acronyms: |
| - | * AD: Alain Durmus. | + | * AD: Alain Durmus. |
| * RD: Randal Douc. | * RD: Randal Douc. | ||
| - | * **What?** The chapters refer to the book: [[https://www.springer.com/gp/book/9783319977034|Markov chains]] by R. Douc, E. Moulines, P. Priouret and P. Soulier. Springer publishers. | + | * **What?** The chapters refer to the book: [[https://www.springer.com/gp/book/9783319977034|Markov chains]] by R. Douc, E. Moulines, P. Priouret and P. Soulier. Springer publishers. |
| * **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 ^ |
| - | | Sept. 26 | (AD) | Chapt. 1 and 2. | Introduction to Markov chains | {{:world:ex1.pdf| Exercise sheet 1}} | 1 | | + | | 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}} | |
| - | | Oct. 3 | (AD) | Chapt. 2 and 3 | Invariance, Reversibility. MCMC. Canonical space. | {{:world:ex_2_2024.pdf| Exercise sheet 2}} | 2 | | + | | 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}} | |
| - | | Oct. 17 | | | Pause | | | | + | | 09/10 | (AD) | | Canonical space (continued). Kolmogorov extension theorem. Strong Markov property. Dynamical systems, Birkhoff theorem | | |
| - | | 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 | | + | | 16/10 | (AD) | Chapt. 3 | Metrics: TV norms, V norms, Wasserstein. | {{:world:ex_3_2024.pdf| Exercise sheet 3}} | |
| - | | Oct. 31 | (AD) | Chap 5 | Ergodic theory and law of large numbers. | Chapitre 3 de ce {{ :world:polymcmc.pdf |polycopié}} | 4/5 | | + | | 23/10 or 30/10 | (RD) | Chap 5 | Geometric ergodicity. | | |
| - | | Nov 14 | (RD) | Chapt. 6 | Atomic chains. Transience, recurrence. Maximum principle. Uniformly transient sets. | | 6 | | + | | 06/11 | (RD) | Chapt. 6 | Central Limit Theorems | | |
| - | | Nov 21 | (RD) | Chap 6 | Period, aperiodicity, positive atoms, null-recurrence, Kac's theorem. | | 7 | | + | | 13/11 | (RD) | Chap 6 | Rosenthal inequalities (Alain). | | |
| - | | Nov 28 | (RD) | Chapt. 6-7-8 | Independent excursions between atoms, coupling inequalities, renewal theory, residual lifetime. | | 8 | | + | | 20/11 | (AD) | Chapt. 6-7-8 | Quantitative Central Limit theorems | | |
| - | | Dec 5 | (RD) | Chapt. 18-19 | Geometric ergodicity. | | 9 | | + | | 27/11 | (RD) | Chapt. 18-19 | Convergence via spectral methods | | |
| - | | Dec 12 | (RD) | Chap 21 | Central limit theorem. | | 10 | | + | | 04/12 | (AD) | Chap 21 | Contractive convergence via curvature lower bounds. | | |
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| <WRAP center round tip 60%> | <WRAP center round tip 60%> | ||
| - | <color /red>{{ :world:polymarkovchains.pdf |LectureNotes2024}}</color> | + | {{ :world:polymarkovchains.pdf |LectureNotes2024}} |
| </WRAP> | </WRAP> | ||
world/markovchains.1733486183.txt.gz · Last modified: 2024/12/06 12:56 by rdouc
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