Fluctuation bounds for chaos plus noise in dynamical systems

Abstract

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 $y_0,...,y_n$, for all $n$. The chaotic systems we consider include for instance the Hénon attractor for Benedicks-Carleson parameters.

17 pages, 2 figures, submitted

References in corpus (3)

• Moment inequalities for functions of independent random variables
• Optimal concentration inequalities for dynamical systems
• Fluctuations of observables in dynamical systems: from limit theorems to concentration inequalities

Cited by in corpus (3)

• Annealed and quenched limit theorems for random expanding dynamical systems
• Extreme Value laws for dynamical systems under observational noise
• Concentration inequalities for sequential dynamical systems of the unit interval