A. Boudou and S. Viguier-Pla (2011)
Processus stationnaires isotropes et leurs mesures
aléatoires associées.
Actes des 43èmes Journées De Statistique, SFDS,
Tunis, 23-27 mai 2011.
- Classification
- 60G57, 60G10, 60B15, 60H05
- Keywords
- Random measures, Stationary processes,
Tensor products, Isotropy, Spectral measures
Abstract :
Many natural phenomenons can be modelized by isotropic stationary processes. Such
processes have been the interest of numerous authors, as for example Yadrenko (1983),
Crujeiras et al. (2008), Stein (2005), Adler (1981) and Cucala et al. (2006).
It is well-known that each stationary process can be associated with one and only one
random measure, by the Fourier Transform. Then, any property of a process expressed in
the time domain have its pending in the frequential domain. We will, in this presentation,
focus our interest to the structure of a random measure associated with such a process,
when it is isotropic. Indead, the isotropic property allows the decomposition of the random
measure as a tensor product of two random measures, one for the radius, and the other
for the direction. We study the properties of this structure.
We then can define classes of isotropic processes. We give an example of family of
isotropic processes, and we illustrate it by simulation.
Résumé détaillé