Mathieu Merle
page web
Courriel : merle@lpsm.paris
Bureau : Sophie Germain 509
Téléphone : 01-57-27-91-49
Université Paris 7
M2
Chaines de Markov

Cours Lu 09h00- 12h00 en salle 2014
Ici, vous trouverez notes de cours, feuilles de TD, et des éléments de correction

  • Examen final, corrigé

  • Exercises (with answers)

  • DST1, corrigé

  • DST2, corrigé

  • Examen 2016, corrigé

  • Examen 2017, corrigé

  • Examen 2019, corrigé

  • Sélection de sujets passés, corrigés

  • Slides, Part 1.1 (Definitions, first properties)

  • Slides, Part 1.2 (Classical and important examples of Markov chains)

  • Slides, Part 1.3 (Invariant measures)

  • Slides, Part 1.4 (Longterm behaviour)

  • Slides, Part 2.1 (Martingales)

  • Slides, Part 2.2 (Potentials)

  • Slides, Part 2.3 (Analogy with electric networks)

  • Slides, Part 2.3.2 (Transience/recurrence of SRW on the integer grid, Polya's proof)

  • Slides, Part 3.1 (Total variation distance)

  • Slides, Part 3.2 (Mixing times)

  • Slides, Part 3.3 (Upper bound of mixing times through coupling)

  • Slides, Part 3.4 (Spectral decomposition for reversible chains)

  • Slides, Part 3.5 (Upper bound of mixing times through hitting times)

  • Slides, Part 3.6 (Lower bounds for mixing times)

  • Slides, Part 4.1 (Continuous-times chains, definition)

  • Slides, Part 4.2 (Markov property for continuous-time chains)

  • Slides, Part 4.3 (Poisson process)

  • Slides, Part 4.4 (Finite state case)

  • Slides, Part 4.5 (Explosion criteria)

  • Slides, Part 4.6 (General case : characterization)

  • Slides, Part 4.7 (General case : properties)