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Article Dans Une Revue Stochastics and Dynamics Année : 2006

Spectral properties of chaotic processes

Bernard Bercu
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Clémentine Prieur

Résumé

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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Dates et versions

hal-00023715 , version 1 (04-05-2006)

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  • HAL Id : hal-00023715 , version 1

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Bernard Bercu, Clémentine Prieur. Spectral properties of chaotic processes. Stochastics and Dynamics, 2006, 6 (3), pp.355-371. ⟨hal-00023715⟩
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