Fluctuation bounds for chaos plus noise in dynamical systems

Details Fluctuation bounds for chaos plus noise in dynamical systems Fluctuation bounds for chaos plus noise in dynamical systems

2011-12-16

arxiv.org/abs/1112.3696v1

Nonlinear Sciences

Chaotic Dynamics

17 pages, 2 figures, submitted

Scientific paper

We are interested in time series of the form $y_{n} = x_{n} + e_{n}$ where $\{x_{n}\}$ is generated by a chaotic dynamical system and where $e_{n}$ 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 H\'{e}non attractor for Benedicks--Carleson parameters.

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