Abstract
The Shannon-MacMillan-Breiman theorem proves the asymptotic equipartition property in typical sets, as soon as the process is ergodic. The notion of ergodicity and Birkhoff's theorem are introduced, but not proved. The main argument of the proof of the asymptotic equipartition theorem for ergodic processes is then explained, without giving details of the proof.
The second part of the lecture introduces the model and definition of Markov chains. The stochastic transition matrix is defined. The invariant stationary law of a Markov chain is then specified, as is its link with reversibility, defined by the detailed balance equation. The examples of random walks and the Ehrenfest urn are explained.
