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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
Department of Mathematics, Boston University, 111 Cummington Street, Boston, MA 02215, USA
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
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

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