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Wavelet analysis and covariance structure of some classes of non-stationary processes. (English) Zbl 0958.60034
Summary: 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.

60G12 General second-order stochastic processes
42C40 Nontrigonometric harmonic analysis involving wavelets and other special systems
46N30 Applications of functional analysis in probability theory and statistics
28A80 Fractals
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