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world:markovchains

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2017/10/07 23:39 · douc

A course on Markov Chains: Advanced topics

Program of the course

  • Where? Institut de Mathématiques d'ORSAY. Room: 1A14.
  • When? Every course will hold on Wednesday from 14H to 18H30 (exact dates are given below).
  • Who? The list of the teachers are given below with their acronyms:
    • EM: Eric Moulines.
    • RD: Randal Douc.
  • What? The chapters refer to the book: Markov chains by R. Douc, E. Moulines, P. Priouret and P. Soulier. Springer publishers.
Date Prof Chapters Topics Material Cours
Sept. 23 (EM) Chapt. 1 and 2. Introduction to Markov chains, invariant measure, reversibility. MCMC. 1
Sept. 30 (RD) Chapt. 3 and 4 Stopping time, canonical space, (Strong) Markov property, Kac formula for invariant probability measures, Harmonic functions, martingales, drift functions. Maximum principle. Tutorial 2 2
Oct. 7 (RD) Chapt. 4 and 6 Solidarity property, comparison theorem, Atomic chains (atoms, recurrence, transience) Tutorial 3 3
Oct. 14 (EM) Chapt 6,7 End of Atomic chains. Coupling results on discrete Markov chains. 4
Oct. 21 (EM) Chapt 8 Renewal theory, Blackwell's and Kendall's theorems. Geometric ergodicity by the renewal approach. 5
Oct. 28 (EM) Chapt. 9 small sets, irreducibility, aperiodicity, 6
Nov. 4 (RD) Chap 11, 18 irreducibility (end…), Splitting, existence of an invariant measure. Tutorial 7 7
Nov. 18 (RD) Chapt. 18 Geometric ergodicity by Hairer's method La preuve d'Hairer se trouve ici Notes de cours 8
Nov 25 (EM) Chapt. 19 Coupling methods and geometric ergodicity 9
Dec. 2 (RD) Chapt. 5 Ergod. Theorem. Pour suivre la visio, veuillez cliquer ici 10

Registration to the course "Markov chains: approfondissements"

Evaluation

Evaluation: It will hold on Wednesday, 6th of January, 2021 from 1.30pm to 6pm. It will consist in a pedagogical course of 1 hour (slides and/or hand written on tablets) and 15 minutes of questions. The possible chapters are in the book in the Part IV (Chapters 20,21,22, 23).

To go to the zoom session associated to the defense, please click here .

Schedule Chapter Groups of 3 Students
13H30-14H00 Chap. 20 Wasserstein Meziane
14H00-15H15 Chap. 23 Concentration inequalities Nathan, Dylan, sixiao zhu
15H15-16H30 Chap. 21 Central Limit theorems Loïc, Issa, Clément
16H30-17H45 Chap. 22 Spectral theory Sixte, Julien et Emmanuel

Contact

name email adresses
Eric Moulines eric.moulines At polytechnique.edu
Randal Douc randal.douc At telecom-sudparis.eu

Discussion

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world/markovchains.txt · Dernière modification: 2021/04/06 09:15 par rdouc