On the spectral density of the wavelet transform of fractional Brownian motion. (English) Zbl 0934.62097

Kato, Takeshi; Masry, Elias

J. Time Ser. Anal. 20, No. 5, 559-563 (1999).

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.

Reviewer: A.Ya.Olenko (Kyïv)

MSC:

62M15

Inference from stochastic processes and spectral analysis

Keywords:

wavelet transforms; fractional Brownian motion; existence of spectral density