Stochastic integral representation and properties of the wavelet coefficients of linear fractional stable motion

Let 0<[alpha][less-than-or-equals, slant]2 and let . Let {X(t),t[set membership, variant]T} be a linear fractional [alpha]-stable (0<[alpha][less-than-or-equals, slant]2) motion with scaling index H (0<H<1) and with symmetric [alpha]-stable random measure. Suppose that [psi] is a bounded real function with compact support [a,b] and at least one null moment. Let the sequence of the discrete wavelet coefficients of the process X beWe use a stochastic integral representation of the process X to describe the wavelet coefficients as [alpha]-stable integrals when H-1/[alpha]>-1. This stochastic representation is used to prove that the stochastic process of wavelet coefficients , with fixed scale index , is strictly stationary. Furthermore, a property of self-similarity of the wavelet coefficients of X is proved. This property has been the motivation of several wavelet-based estimators for the scaling index H.