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On the Spectral Density of the Wavelet Transform of Fractional Brownian Motion
Author(s) -
Kato Takeshi,
Masry Elias
Publication year - 1999
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/1467-9892.00157
Subject(s) - mathematics , fractional brownian motion , wavelet , wavelet transform , brownian motion , spectral density , mathematical analysis , scale (ratio) , statistical physics , statistics , artificial intelligence , computer science , physics , quantum mechanics
We consider the wavelet transform { W a ( t ), −∞ < t } < ∞}, at scale a > 0, of a fractional Brownian motion. A simple and mathematically rigorous proof is given to establish the existence of the spectral density f Wa (λ) of the wavelet transform and provide an expression for it.