Limit theorems and inequalities via martingales methods
Résumé
In these notes, we first give a brief overwiew of martingales methods, from Paul Lévy
(1935) untill now, to explain why these methods have become a central tool in probability, statistics and
ergodic theory. Next, we present some recent results for/or based on martingales: exponential bounds
for super-martingales, concentration inequalities for Lipschitz functionals of dynamical systems, oracle
inequalities for the Cox model in a high dimensional setting, and invariance principles for stationary
sequences.