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

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}t∈R is a collection of deterministic functions and {n}n∈Z 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