Fluctuation bounds for chaos plus noise in dynamical systems
Maldonado, Cesar
Original · EN
We are interested in time series of the form yₙ = xₙ + ξₙ where xₙ is generated by a chaotic dynamical system and where ξₙ 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 y₀,..., yₙ, for all n. The chaotic systems we consider include for instance the Hénon attractor for Benedicks-Carleson parameters.
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