On some problems related to machine-generated noise

Computer calculations do not exactly follow classical theoretical models: it is enough to think of rounding errors or of pseudo-random number generators, typically chaotic maps, simulating iid noise. The thesis aims to look at their impacts on statistical inference. We prove that the attractors of dynamical systems are stable under some kind of infinitesimal random perturbation which is a good approximation to the rounding errors. Concerning the autoregressive models, we have obtained the asymptotic bias and the limiting distribution for the Yule-Walker estimator of the autoregressive parameter under considerably weaker assumption than that of independence in the noise sequence. In the same way, we have proved consistency and asymptotic normality of the linear regression estimator for quite general chaos driven linear stochastic regression models. In particular, these suggest robustness of the corresponding classical asymptotic results and throw some light on the use of simulations in verifying these results.