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Stochastic Processes and their Applications 86 (2000) 177182 www.elsevier.com/locate/spa

Summary: Stochastic Processes and their Applications 86 (2000) 177­182
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
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 =
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


Source: Abry, Patrice - Laboratoire de Physique, Ecole Normale Supérieure de Lyon


Collections: Engineering