Extreme Value laws for dynamical systems under observational noise

In this paper we prove the existence of Extreme Value Laws for dynamical systems perturbed by instrument-like-error, also called observational noise. The instrument characteristics defined as precision and accuracy act both by truncating and randomly displacing the real value of the measured observable. Here we analyse both the effects from a theoretical and numerical point of view. Classical Extreme Value Laws can be found in this case but their normalizing parameters depend on the intensity of the noise. Numerical experiments support the theoretical findings and give an indication of the order of magnitude of the perturbation needed to observe relevant deviations from the deterministic dynamics creating a gateway for defining new rigorous techniques for studying extreme events of experimental time series. Contrary to the claims of several papers where noise addition let the orbits asymptotically fill the ambient space thus losing information about any fractal structures of the attractor, here we show instead that observational noise can be used to recover fractal dimensions.