Beneath the noise, chaos

DOI10.1214/aos/1018031203zbMath0980.62085OpenAlexW2071091379MaRDI QIDQ1970474

Steven P. Lalley

Publication date: 6 March 2002

Published in: The Annals of Statistics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1214/aos/1018031203

zbMATH Keywords

hyperbolic attractornonlinear filternoise reductionAxiom A system

Mathematics Subject Classification ID

Inference from stochastic processes and prediction (62M20) Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.) (37D20) Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45) Time series analysis of dynamical systems (37M10)

Related Items

Prediction of dynamical time series using kernel based regression and smooth splines, A Bayesian nonparametric approach to dynamical noise reduction, Statistical inference for dynamical systems: a review, Empirical risk minimization and complexity of dynamical models, Denoising signals corrupted by chaotic noise, Finitary reconstruction of a measure preserving transformation, On concentration properties of partially observed chaotic systems, Consistency of support vector machines for forecasting the evolution of an unknown ergodic dynamical system from observations with unknown noise, Extreme value laws for dynamical systems under observational noise, Topology-based denoising of chaos, Consistency of maximum likelihood estimation for some dynamical systems, Convergence properties of gradient descent noise reduction, Rising Above Chaotic Likelihoods, Gibbs posterior convergence and the thermodynamic formalism

Cites Work

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• Stable and Random Motions in Dynamical Systems
• Differential Topology
• Ergodic theory of chaos and strange attractors
• Equilibrium states and the ergodic theory of Anosov diffeomorphisms
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