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Abstract : 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.

Keywords : wavelet analysis stationary processes locally stationary processes stationary increments fractional increments fractional Brownian motion





Autor: Charles-Antoine Guérin -

Fuente: https://hal.archives-ouvertes.fr/



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