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Article Dans Une Revue Journal of Fourier Analysis and Applications Année : 2000

Wavelet analysis and covariance structure of some classes of non-stationary processes

Charles-Antoine Guérin

Résumé

Processes with stationary n-increments are known to be characterized by the stationarity of their continuous wavelet coefficients. We extend this result to the case of processes with stationary fractional increments and locally stationary processes. Then we give two applications of these properties. First, we derive the explicit covariance structure of processes with stationary n-increments. Second, for fractional Brownian motion, the stationarity of the fractional increments of order greater than the Hurst exponent is recovered.
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hal-00083193 , version 1 (10-07-2016)

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Charles-Antoine Guérin. Wavelet analysis and covariance structure of some classes of non-stationary processes. Journal of Fourier Analysis and Applications, 2000, 6 (4), pp.403-425. ⟨10.1007/BF02510146⟩. ⟨hal-00083193⟩
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