Wavelet analysis and covariance structure of some classes of non-stationary processes |
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Authors: | Charles-Antoine Guérin |
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Institution: | 1. Department of Mathematics and Statistics, Chalmers University of Technology, S-41296, Gothenburg, Sweden 2. Laboratoire d'Optique Electromagnétique, Faculté des Sciences de Saint-Jér?me, case 162, F-13397, Marseille cedex 20
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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. |
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Keywords: | 42A38 42A82 46F 46N30 60G12 |
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