Spectral properties of chaotic processes

Abstract : We investigate the spectral asymptotic properties of the stationary dynamical system $\xi_t=\varphi(T^t(X_0))$. This process is given by the iterations of a piecewise expanding map $T$ of the interval $[0,1]$, invariant for an ergodic probability $\mu$. The initial state $X_0$ is distributed over $[0,1]$ according to $\mu$ and $\varphi$ is a function taking values in $\R$. We establish a strong law of large numbers and a central limit theorem for the integrated periodogram as well as for Fourier transforms associated with $(\xi_t)$. Several examples of expanding maps $T$ are also provided.
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Contributor : Bernard Bercu <>
Submitted on : Tuesday, January 1, 2008 - 7:20:35 PM
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  • HAL Id : hal-00201620, version 1


Bernard Bercu, Clémentine Prieur. Spectral properties of chaotic processes. Stochastics and Dynamics, World Scientific Publishing, 2006, 6 (3), pp.355-371. ⟨hal-00201620⟩



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