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Fluctuation bounds for chaos plus noise in dynamical systems

We are interested in time series of the form $y_{n} = x_{n} + ξ_{n}$ where ${x_{n}}$ is generated by a chaotic dynamical system and where $ξ_{n}$ 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 $y_{0}, ..., y_{n}$, for all $n$. The chaotic systems we consider include for instance the Hénon attractor for Benedicks-Carleson parameters.