Processus aléatoires et applications -- Algorithmes MCMC et vitesse de convergence

Abstract

Lecture notes (in French) of a master 2 level course in applied mathematics. Contents: Part I. Markov chains on a countable space. 1. Examples 2. Summary of basic properties. 3. Spectral theory and speed of convergence. 4. Lyapunov functions and speed of convergence. 5. MCMC algorithms. Part II. Markov chains on continuous space. 6. Definitions and examples. 7. Invariant probability and speed of convergence.

89 pages, in French language, 10 figures