world:markovchains
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world:markovchains [2025/09/12 15:31] rdouc [Table] |
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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, first definitions, Markov kernel, Elementary operations. Invariant measures / reversibility | {{:world:ex1.pdf| Exercise sheet 1}} | 1 | | + | | 1 | (AD) | Chapt. 1 and 2. | Introduction to Markov chains, first definitions, Markov kernel, Elementary operations. Invariant measures / reversibility | {{:world:ex1.pdf| Exercise sheet 1}} | 1 | |
| - | | Oct. 3 | (AD) | Chapt. 2 and 3 | Canonical space. Kolmogorov extension theorem. Strong Markov property. | {{:world:ex_2_2024.pdf| Exercise sheet 2}} | 2 | | + | | 2 | (AD) | Chapt. 2 and 3 | Canonical space. Kolmogorov extension theorem. Strong Markov property.Applications of the Markov properties: Stopping times. | {{:world:ex_2_2024.pdf| Exercise sheet 2}} | 2 | |
| - | | Oct. 17 | | | Pause | | | | + | | 3 | (AD) | | 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 | | + | | 4 | (AD) | Chapt. 3 | Metrics: TV norms, V norms, Wasserstein. | {{:world:ex_3_2024.pdf| Exercise sheet 3}} | 3 | |
| - | | Oct. 31 | (AD) | Chap 5 | Ergodic theory and law of large numbers. | Chapitre 3 de ce {{ :world:polymcmc.pdf |polycopié}} | 4/5 | | + | | Oct. 31 | (RD) | Chap 5 | Geometric ergodicity. | Chapitre 3 de ce {{ :world:polymcmc.pdf |polycopié}} | 4/5 | |
| - | | Nov 14 | (RD) | Chapt. 6 | Atomic chains. Transience, recurrence. Maximum principle. Uniformly transient sets. | | 6 | | + | | Nov 14 | (RD) | Chapt. 6 | Central Limit Theorems | | 6 | |
| - | | Nov 21 | (RD) | Chap 6 | Period, aperiodicity, positive atoms, null-recurrence, Kac's theorem. | | 7 | | + | | Nov 21 | (RD) | Chap 6 | Rosenthal inequalities (Alain). | | 7 | |
| - | | Nov 28 | (RD) | Chapt. 6-7-8 | Independent excursions between atoms, coupling inequalities, renewal theory, residual lifetime. | | 8 | | + | | Nov 28 | (AD) | Chapt. 6-7-8 | Quantitative Central Limit theorems | | 8 | |
| - | | Dec 5 | (RD) | Chapt. 18-19 | Geometric ergodicity. | | 9 | | + | | Dec 5 | (RD) | Chapt. 18-19 | Convergence via spectral methods | | 9 | |
| - | | Dec 12 | (RD) | Chap 21 | Central limit theorem. | | 10 | | + | | Dec 12 | (AD) | Chap 21 | Contractive convergence via curvature lower bounds. | | 10 | |
world/markovchains.txt · Last modified: 2025/09/12 15:58 by rdouc
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