Appears in collection : Extreme value theory and laws of rare events / Théorie des valeurs extrêmes et lois des évènements rares

We study law of rare events for random dynamical systems. We obtain an exponential law (with respect to the invariant measure of the skew-product) for super-polynomially mixing random dynamical systems. For random subshifts of finite type, we analyze the distribution of hitting times with respect to the sample measures. We prove that with a superpolynomial decay of correlations one can get an exponential law for almost every point and with stronger mixing assumptions one can get a law of rare events depending on the extremal index for every point. (These are joint works with Benoit Saussol and Paulo Varandas, and Mike Todd).