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A course on Markov Chains: Advanced topics

Registration to the course

Student Projects on Markov chains

Program of the course

  • Where? Institut de Mathématiques d'ORSAY. Room: 1A14.
  • When? Every course will hold on Thursday from 9H to 12H00 (exact dates are given below).
  • Who? The list of the teachers are given below with their acronyms:
    • AD: Alain Durmus.
    • RD: Randal Douc.
  • What? The chapters refer to the book: Markov chains by R. Douc, E. Moulines, P. Priouret and P. Soulier. Springer publishers.
Prof Chapters Topics Material Cours
Sept. 21 (AD) Chapt. 1 and 2. Introduction to Markov chains, invariant measure, 1
Sept. 28 (AD) Chapt. 2 and 3 Reversibility. MCMC. Canonical space. Stopping time, (Strong) Markov property 2
Oct. 5 (AD) Chapt. 3 Harmonic functions, martingales, drift functions. Maximum principle, Solidarity property. Comparison theorem. 3
Oct. 12 (AD) Chapt 6,7 Atomic chains (atoms, recurrence, transience). 4
Oct 19 (AD) Chapt 8 Renewal theory, Blackwell's and Kendall's theorems. Geometric ergodicity by the renewal approach. 5
Nov 9 (RD) Chapt. 9 small sets, irreducibility, aperiodicity, 6
Nov 16 (RD) Chap 11, 18 irreducibility (end…), Splitting, existence of an invariant measure. Tutorial 7 7
Nov 23 (RD) Chapt. 5 Ergod. Theorem. Notes de cours Chapitre 3 de ce polycopié 8
Nov 30 (RD) Chapt. 18 Geometric ergodicity by Hairer's method La preuve d'Hairer se trouve ici Notes de cours 9
Dec 7 (RD) Chapt. 19 Coupling methods and geometric ergodicity 10

Example of an examination


name email adresses
Alain Durmus alain.durmus “Arobase” polytechnique.edu
Randal Douc randal.douc “Arobase” polytechnique.edu


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world/markovchains.txt · Last modified: 2023/12/03 22:13 by rdouc