On the Spectral Degeneracy of Wavelet Transforms of Fractional Brownian Motion
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Existence of spectral density of wavelet transform in the case of fractional Brownian motion is proved by Kato and Masry (1999). Given their results, we provide supplementary results on spectral behavior at thezero frequency. It is found that the spectral density at the zero frequency, determined by the memory parameter and the number of vanishing moments of the wavelets, generates possible degeneracy. Our results can be understood as spectral version of decorrelation properties of wavelet transforms.
Abstract
Existence of spectral density of wavelet transform in the case of fractional Brownian motion is proved by Kato and Masry (1999). Given their results, we provide supplementary results on spectral behavior at thezero frequency. It is found that the spectral density at the zero frequency, determined by the memory parameter and the number of vanishing moments of the wavelets, generates possible degeneracy. Our results can be understood as spectral version of decorrelation properties of wavelet transforms.
참고문헌 (9)
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