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

  • Charles-Antoine Guérin
Article

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.

Math Subject Classifications

42A38 42A82 46F 46N30 60G12 

Keywords and Phases

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

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Copyright information

© Birkhäuser 2000

Authors and Affiliations

  • Charles-Antoine Guérin
    • 1
    • 2
  1. 1.Department of Mathematics and StatisticsChalmers University of TechnologyGothenburgSweden
  2. 2.Laboratoire d'Optique ElectromagnétiqueFaculté des Sciences de Saint-JérômeMarseille cedex 20

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