Spectral representation of some non stationary alpha-stable processes

2008/02/21 by Nourddine Azzaoui, Azzaoui, Nourddine
Engineering · Mathematics · Physics and Astronomy · #FOS: Mathematics #Fault Detection and Control Systems #Probability (math.PR) #Quantum chaos and dynamical systems #Radioactive Decay and Measurement Techniques #Statistics Theory (math.ST) #math.PR #math.ST #stat.TH

paper · pdf · doi:10.48550/arxiv.0802.2998

arxiv created 2008/02/21 · openalex publication_date 2008/02/21 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we give a new covariation spectral representation of some non stationary symmetric α-stable processes (SαS). 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 SαS processes (see Cambanis (1983)) or with respect to the general concept of independently scattered SαS measures (Samorodnitsky and Taqqu 1994). Relying on this result we investigate the non stationarity structure of some harmonisable SαS processes especially those having periodic or almost-periodic covariation functions.

Related

• Non-ergodic statistics and spectral density estimation for stationary real harmonizable symmetric α-stable processes
• A paradox on the spectral representation of stationary random processes
• Applications of a simple but useful technique to stochastic convolution of α-stable processes
• Signals Featuring Harmonics with Random Frequencies -- Spectral, Distributional and Ergodic Properties
• Spectral Representation of Multivariate Regularly Varying L 'evy and\n CARMA processes