Can continuous-time stationary stable processes have discrete linear representations?

Vladas Pipiras, Murad S. Taqqu and Patrice Abry

Statistics & Probability Letters, 2003, vol. 64, issue 2, 147-157

Abstract: We show that a non-trivial continuous-time strictly [alpha]-stable, [alpha][set membership, variant](0,2), stationary process cannot be represented in distribution as a discrete linear processwhere is a collection of deterministic functions and are independent strictly [alpha]-stable random variables. Analogous results hold for self-similar strictly [alpha]-stable processes and for strictly [alpha]-stable processes with stationary increments. As a consequence, the usual wavelet decomposition of Gaussian self-similar processes cannot be extended to the [alpha]-stable, [alpha]

Keywords: Stable; processes; Self-similarity; Stationarity; Minimal; spectral; representations; Flows; Cocycles (search for similar items in EconPapers)
Date: 2003
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Citations: View citations in EconPapers (3)

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