 
Summary: Stochastic Processes and their Applications 86 (2000) 177182
www.elsevier.com/locate/spa
Stochastic integral representation and properties of the
wavelet coe cients of linear fractional stable motion
Lieve Delbeke
, Patrice Abry
Royal Meteorological Institute of Belgium, Department of Meteorological Research and Development,
Ringlaan 3, 1180 Brussels, Belgium
Received 3 July 1997; received in revised form 15 July 1999
Abstract
Let 0 ¡ 62 and let T R. Let {X (t); t T} be a linear fractional stable (0 ¡ 62)
motion with scaling index H (0 ¡ H ¡ 1) and with symmetric stable random measure. Suppose
that is a bounded real function with compact support [a; b] and at least one null moment. Let
the sequence of the discrete wavelet coe cients of the process X be
Dj;k =
R
X (t) j;k (t) dt; j; k Z :
We use a stochastic integral representation of the process X to describe the wavelet coe cients
as stable integrals when H  1= ¿  1. This stochastic representation is used to prove that
the stochastic process of wavelet coe cients {Dj;k ; k Z}, with ÿxed scale index j Z, is
