Statistical properties of a skew product with a curve of neutral points

2003/11/12 by Sébastien Gouëzel, Sebastien Gouezel, Gouezel, Sebastien · 1 citation
Economics, Econometrics and Finance · Mathematics · #37A50 #37C40 #60F05 #Dynamical Systems (math.DS) #FOS: Mathematics #Financial Risk and Volatility Modeling #Random Matrices and Applications #Statistical Methods and Inference #math.DS #msc:37A50 #msc:37C40 #msc:60F05

paper · pdf · doi:10.48550/arxiv.math/0311193

32 pages

arxiv created 2003/11/12 · openalex publication_date 2003/11/12 · arxiv updated 2009/12/01 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28

Abstract

We study a skew product with a curve of neutral points. We show that there exists a unique absolutely continuous invariant probability measure, and that the Birkhoff averages of a sufficiently smooth observable converge to a normal law or a stable law, depending on the average of the observable along the neutral curve.

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• Nonstandard functional central limit theorem for nonuniformly hyperbolic dynamical systems, including Bunimovich stadia

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