# Spectral representation of some non stationary alpha-stable processes

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Abstract : In this paper, we give a new covariation spectral representation of some non stationary symmetric $\alpha$-stable processes (S$\alpha$S). This representation is based on a weaker covariation pseudo additivity condition which is more general than the condition of independence. This work can be seen as a generalization of the covariation spectral representation of processes expressed as stochastic integrals with respect to independent increments S$\alpha$S processes (see Cambanis (1983)) or with respect to the general concept of independently scattered S$\alpha$S measures (Samorodnitsky and Taqqu 1994). Relying on this result we investigate the non stationarity structure of some harmonisable S$\alpha$S processes especially those having periodic or almost-periodic covariation functions.
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https://hal.archives-ouvertes.fr/hal-00257920
Contributor : Nourddine Azzaoui <>
Submitted on : Wednesday, February 20, 2008 - 4:19:47 PM
Last modification on : Friday, June 8, 2018 - 2:50:07 PM
Long-term archiving on : Thursday, May 20, 2010 - 11:07:16 PM

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• HAL Id : hal-00257920, version 1
• ARXIV : 0802.2998

### Citation

Nourddine Azzaoui. Spectral representation of some non stationary alpha-stable processes. 2007. ⟨hal-00257920⟩

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