Fluctuation bounds for chaos plus noise in dynamical systems

We are interested in time series of the form $y_n=x_n+{\xi }_n$ where $x_n$ is generated by a chaotic dynamical system and where ${\xi }_n$ models observational noise. Using concentration inequalities, we derive fluctuation bounds for the auto-covariance function, the empirical measure, the kernel density estimator and the correlation dimension evaluated along $y_{0}, …, y_{n}$,forall$n$. The chaotic systems we consider include for instance the H'{e}non attractor for Benedicks-Carleson parameters.