✦ LIBER ✦
Can continuous-time stationary stable processes have discrete linear representations?
✍ Scribed by Vladas Pipiras; Murad S. Taqqu; Patrice Abry
- Publisher
- Elsevier Science
- Year
- 2003
- Tongue
- English
- Weight
- 265 KB
- Volume
- 64
- Category
- Article
- ISSN
- 0167-7152
No coin nor oath required. For personal study only.
✦ Synopsis
We show that a non-trivial continuous-time strictly -stable, ∈ (0; 2), stationary process cannot be represented in distribution as a discrete linear process
where {f t } 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 processes cannot be extended to the -stable, ¡ 2 case.