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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 5 Atomic chains (continued) 5
Nov 9 (RD) Chapt. 8 Ergodic theory. Chapitre 3 de ce polycopié 6
Nov 16 (RD) Chap 9 Renewal theory, Kac's theorem 7
Nov 23 (RD) Postponed 8
Nov 30 (RD) Chapt. 9 Blackwell's and Kendall's theorem 9
Dec 7 (RD) Chapt. 19 Coupling methods, small sets and geometric ergodicity polycopié 10
Dec 14 (RD) Chap 19 End of geometric ergodicity. Revision's exercises.

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: 2024/01/09 13:29 by rdouc