Discrete-Time Stable Processes and Their Certain Properties
Hosoya, Yuzo
Ann. Probab., Tome 6 (1978) no. 6, p. 94-105 / Harvested from Project Euclid
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In this paper we derive the characteristic functions of multivariate stable distributions; specifically the canonical representation of symmetric stable laws is given. Based on that representation, we construct linear stable processes (which include autoregressive stable processes) and stable processes with spectral representation. A sufficient condition for linear stable processes to be regular is given; the complete regularity of autoregressive stable processes is proved. Furthermore, we derive the asymptotic distribution of the Fourier transform of a sample from stable processes with spectral representation.
Publié le : 1978-02-14
Classification:  Stable process,  multivariate symmetric stable distributions,  spectral representation,  regularity,  characteristic function,  Fourier transformation,  60G05,  60G10 
@article{1176995613,
     author = {Hosoya, Yuzo},
     title = {Discrete-Time Stable Processes and Their Certain Properties},
     journal = {Ann. Probab.},
     volume = {6},
     number = {6},
     year = {1978},
     pages = { 94-105},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176995613}
}

Hosoya, Yuzo. Discrete-Time Stable Processes and Their Certain Properties. Ann. Probab., Tome 6 (1978) no. 6, pp.  94-105. http://gdmltest.u-ga.fr/item/1176995613/