Table of Contents

A course on Markov Chains: Advanced topics

Registration to the course

Program of the course

Prof Chapters Topics Material
25/09 (AD) Chapt. 1 and 2. Conditional distribution, their construction and related operations. Introduction to Markov chains, first definitions Exercise sheet 1 Lecture notes Notes Monte Carlo
02/10 (AD) Chapt. 2 and 3 Invariant measures / reversibility, Canonical space. Exercise sheet 2 Exercise sheet 3 Reminders Conditonal expectation Exercises conditional expectation
09/10 (AD) Chap 3 Canonical space (continued). Kolmogorov extension theorem. Strong Markov property. Exercise sheet 4
16/10 (AD) Chapt. 3 Stopping times, return and hitting times, consequences of Markov property. Exercise sheet 5
23/10 (AD) Chap 5 Dynamical systems, Birkhoff theorem, Law of Large Number for Markov chains
06/11 (RD) Chapt. 6 Central Limit Theorems
13/11 (RD) Chap 6 Rosenthal inequalities (Alain).
20/11 (AD) Chapt. 6-7-8 Quantitative Central Limit theorems
27/11 (RD) Chapt. 18-19 Convergence via spectral methods
04/12 (AD) Chap 21 Contractive convergence via curvature lower bounds.

Lecture notes Session 6-7-8-9

Example of an examination

Projects

Contact

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