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Statistics & Probability Letters 64 (2003) 147157 Can continuous-time stationary stable processes have discrete
 

Summary: Statistics & Probability Letters 64 (2003) 147­157
Can continuous-time stationary stable processes have discrete
linear representations?
Vladas Pipirasa, Murad S. Taqqua;, Patrice Abryb
a
Department of Mathematics, Boston University, 111 Cummington Street, Boston, MA 02215, USA
b
Laboratoire de Physique, CNRS UMR 5672, Ecole Normale SupÃerieure de Lyon, 69 364 Lyon Cedex 07, France
Received May 2002; received in revised form April 2003
Abstract
We show that a non-trivial continuous-time strictly -stable, (0; 2), stationary process cannot be repre-
sented in distribution as a discrete linear process

n=-
ft(n) n; t R;
where {ft}tR is a collection of deterministic functions and { n}nZ are independent strictly -stable random
variables. Analogous results hold for self-similar strictly -stable processes and for strictly -stable processes
with stationary increments. As a consequence, the usual wavelet decomposition of Gaussian self-similar pro-
cesses cannot be extended to the -stable, ¡ 2 case.
c 2003 Elsevier B.V. All rights reserved.

  

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

 

Collections: Engineering