  We consider the Ornstein-Uhlenbeck process with a broad initial probability
distribution (Levy distribution), which exhibits so-called non-spectral modes.
The relaxation of such modes differs from those determined from the parameters
of the corresponding Fokker-Planck equation. The first non-spectral mode is
shown to govern the relaxation process and allows for estimation of the initial
distribution's Levy index. A method based on continuous wavelet transformation
is proposed to extract both (spectral and non-spectral) relaxation rates from a
stochastic data sample.
