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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).

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: 2021/05/18 00:35 par rdouc