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RESEARCH PRODUCT
Devroye Inequality for a Class of Non-Uniformly Hyperbolic Dynamical Systems
Jean-rené ChazottesPierre ColletBernard Schmittsubject
Pure mathematicsClass (set theory)[MATH.MATH-PR] Mathematics [math]/Probability [math.PR]Dynamical systems theoryLorentz transformation[MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS][ MATH.MATH-DS ] Mathematics [math]/Dynamical Systems [math.DS]General Physics and AstronomyHölder condition[MATH.MATH-DS] Mathematics [math]/Dynamical Systems [math.DS]Of the formDynamical Systems (math.DS)01 natural sciencesUpper and lower bounds010104 statistics & probabilitysymbols.namesakeFOS: Mathematics0101 mathematicsMathematics - Dynamical SystemsMathematical PhysicsMathematicsApplied Mathematics010102 general mathematicsProbability (math.PR)Statistical and Nonlinear PhysicsObservableFunction (mathematics)[MATH.MATH-PR]Mathematics [math]/Probability [math.PR]symbols[ MATH.MATH-PR ] Mathematics [math]/Probability [math.PR]Mathematics - Probabilitydescription
In this paper, we prove an inequality, which we call "Devroye inequality", for a large class of non-uniformly hyperbolic dynamical systems (M,f). This class, introduced by L.-S. Young, includes families of piece-wise hyperbolic maps (Lozi-like maps), scattering billiards (e.g., planar Lorentz gas), unimodal and H{\'e}non-like maps. Devroye inequality provides an upper bound for the variance of observables of the form K(x,f(x),...,f^{n-1}(x)), where K is any separately Holder continuous function of n variables. In particular, we can deal with observables which are not Birkhoff averages. We will show in \cite{CCS} some applications of Devroye inequality to statistical properties of this class of dynamical systems.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2005-06-17 |