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On the spectral density of the wavelet transform of fractional Brownian motion. (English) Zbl 0934.62097
The authors consider the fractional Brownian motion process \(\{X(t),\;t\in R\}.\) The wavelet transform at scale \(a>0:\) \[ W_a(t)=a^{-1/2}\int_{-\infty}^{+\infty}X(u)\overline{\psi}((u-t)/a)du \] is studied. Conditions for the existence of the spectral density \(f_{W_a}(\lambda)\) and an expression for it are given.

MSC:
62M15 Inference from stochastic processes and spectral analysis
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