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

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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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Authors and Affiliations

  1. Department of Mathematics and Statistics, Chalmers University of Technology, S-41296, Gothenburg, Sweden

    Charles-Antoine Guérin

  2. Laboratoire d'Optique Electromagnétique, Faculté des Sciences de Saint-Jérôme, case 162, F-13397, Marseille cedex 20

    Charles-Antoine Guérin

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  1. Charles-Antoine Guérin
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Communicated by C. Houdré

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Guérin, CA. Wavelet analysis and covariance structure of some classes of non-stationary processes. The Journal of Fourier Analysis and Applications 6, 403–425 (2000). https://doi.org/10.1007/BF02510146

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  • DOI: https://doi.org/10.1007/BF02510146

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